View source for Olympiad books

Here is a list of '''Olympiad Books''' that have Olympiad-level problems used to train students for future [[mathematics]] competitions.

You can discuss [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=405377 here] about these books or request new books. Let's categorize books into '''Theory''' books, '''Problem''' books, and '''Both''' books.

==Algebra==
===Inequalities===
*''Secrets In Inequalities volume 1 - Basic Inequalities'' - '''Pham Kim Hung'''.
*''Secrets In Inequalities volume 2 - Advanced Inequalities'' - '''Pham Kim Hung'''.
*''Algebraic Inequalities - Old And New Methods'' -  '''Vasile Cirtoaje'''.
*''Old And New inequalities volume 1'' - '''Titu Andreescu, Vasile Cirtoaje, Gabriel Dospinescu, Mircea Lascu'''.
*''Old And New Inequalities volume 2'' - '''Vo Quoc Ba Can, Cosmin Pohoata'''.
*''The Cauchy-Schwarz Master Class'' - '''J. Michael Steele'''.
*''Inequalities: A Mathematical Olympiad Approach'' - '''Radmila Bulajich Manfrino, Jose Antonio Ortega, Rogelio Valdez Delgado'''.
*''An Introduction to Inequalities'' - '''Bellman, Beckenbach'''.
*''Analytic Inequalities'' - '''Mitrinovic'''.
*[http://www.artofproblemsolving.com/Forum/viewforum.php?f=55 ''Inequalities Theorems and Formulas'' forum].
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=7942 ''Useful Inequalities''] topic.

===Polynomials===
*[http://www.amazon.com/Polynomials-Polynomial-Inequalities-Graduate-Mathematics/dp/0387945091/ref=sr_1_3?s=books&ie=UTF8&qid=1304702384&sr=1-3 ''Polynomials and Polynomial Inequalities (Graduate Texts in Mathematics)''] - (Springer) - '''Peter Borwein - Tamas Erdely'''.

*[http://www.amazon.com/Geometry-Polynomials-Mathematical-Surveys-Monographs/dp/0821815032/ref=cm_cr_pr_product_top ''Geometry of Polynomials''] - (American Mathematical Society) - '''Morris Marden'''.

*[http://www.amazon.com/Polynomials-Problem-Books-Mathematics-Barbeau/dp/0387406271/ref=cm_cr_pr_product_top ''Polynomials''] - (Springer) - '''E.J. Barbeau'''.
*[http://www.amazon.com/Solving-Polynomial-Equations-Foundations-Applications/dp/3642063616/ref=sr_1_5?s=books&ie=UTF8&qid=1304702384&sr=1-5 Solving Polynomial Equations: Foundations, Algorithms, and Applications] - (Springer) - '''Alicia Dickenstein - Ioannis Z. Emiris'''.

===Functional Equations===
*[https://parvardi.com/FE2018 ''Functional Equations in Mathematical Olympiads (2017 - 2018): Problems and Solutions (Vol. I)''] - (Amazon) -  '''Amir Hossein Parvardi'''.
*[https://www.worldscientific.com/worldscibooks/10.1142/4875 ''Functional Equations and Inequalities in Several Variables''] - (World Scientific Publication) -  '''Stefan Czerwik'''.
*[https://www.elsevier.com/books/lectures-on-functional-equations-and-their-applications/aczel/978-0-12-043750-4 ''Lectures on Functional Equations''] - (Academic Press) -  '''J. Aczel'''.
*[https://www.amazon.in/Functional-Equations-Revised-Updated-2nd/dp/8172867816 ''Functional Equations: A Problem Solving Approach''] - (Prism Books) -  '''B.J. Venkatchala'''.
*[https://www.springer.com/gp/book/9780387345345 ''Functional Equations and How to Solve Them''] - (Springer) - '''Christopher G. Small'''.

==Number Theory==


*''Number Theory Structures, Examples, and Problems'' - '''Titu Andreescu, Dorin Andrica''' - '''Both''' Book (olympiad examples followed by problems). '''Excellent''' book for number theory.
*''An Introduction to Diophantine Equations'' - '''Titu Andreescu, Dorin Andrica, Ion Cucurezeanu''' - '''Both''' Book (olympiad examples followed by problems). '''Excellent''' book for Diophantine equations.
*''104 Number Theory Problems'' - '''Titu Andreescu, Dorin Andrica, Zuming Feng''' - '''Both''' Book.
*''250 problems in number theory'' - '''W. Sierpinski''' - '''Problem''' Book.

*''A Selection of Problems in Theory of Numbers'' - '''W. Sierpinski''' - '''Problem''' Book. '''Great''' book.
*''The Theory of Numbers - a Text and Source Book of Problems'' - '''Andrew Adler, John E. Coury''' - '''Both''' Book (olympiad examples followed by problems). '''Excellent''' book.
*''[http://parvardi.com/download/number-theory-naoki-sato/ Number Theory]'' - '''Naoki Sato (nsato)''' - '''Theory''' Book.
*''Solved and Unsolved Problems in Number Theory'' - '''Daniel Shanks''' - '''Problem''' Book.
*''Elementary Number Theory (Revised Printing)'' - '''David M. Burton''' - ''' It is a nice book for theory building and is low-impact in its approach.
*''An Introduction to the Theory of Numbers'' - '''Ivan Niven, Herbert S. Zuckerman''' - '''Theory''' Book.
*''Elementary Number Theory'' - '''W. Edwin Clark''' [free online - [http://parvardi.com/download/elementary-number-theory-w-edwin-clark/ '''download here''']] - '''Theory''' Book.
*''Numbers and Curves'' - '''Franz Lemmermeyer''' [free online - [http://parvardi.com/download/numbers-and-curves-franz-lemmermeyer/ '''download here''']] - '''Theory''' Book.
*''Algorithmic Number Theory'' - '''S. Arun-Kumar''' [free online - [http://parvardi.com/download/algorithmic-number-theory-s-arun-kumar/ '''download here''']] - '''Theory''' Book.
*''Elementary Number Theory'' - '''William Stein''' - [free online - [http://parvardi.com/download/elementary-number-theory-william-stein/ '''download here''']] - '''Both''' Book (lots of theorems with problems at the end of each section).
*''Number Theory, An Introduction via the Distribution of Primes'' - '''Benjamin Fine, Gerhard Rosenberger''' - '''Theory''' Book.
*''Number Theory for Computing'' - '''Song Y. Yan''' - '''Theory''' Book (this book contains computational examples/theorems for number theory).
*''Pell's Equation'' - '''Edward J. Barbeau''' [level is a little above olympiad] - '''Both''' Book (olympiad examples followed by problems).

==Geometry==

*''103 Trigonometry Problems'' - '''Titu Andreescu, Zuming Feng''' - '''Both''' book (solved examples and approaches + problems).
*''Triangles, Concurrency and Quadrilaterals'' - [free online - [http://www.artofproblemsolving.com/Forum/download/file.php?id=33191 '''download here''']].
*''Geometry Unbound'' - '''Kedlaya''' - '''Theory''' book - this book is available online for download. See [http://www-math.mit.edu/~kedlaya/geometryunbound/ '''here'''l] - '''Great''' book.
*''Famous Problems of Geometry and How to Solve Them'' - '''Benjamin Bold''' - '''Both''' book (solved examples and approaches + problems).
*''Challenging Problems in Geometry'' - '''Alfred S. Posamenter, Charles T. Salkind''' - '''Both''' book - '''Great''' book.
*''Euclidean Geometry in Mathematical Olympiads'' - '''Evan Chen''' - '''Both''' book - '''Excellent''' book.
*''Elements of Projective Geometry'' - '''Luigi Ceremona''' - '''Both''' book, again.
*''Japanese Temple Geometry Problems'' - '''San Gaku''' - '''Problem''' book (it contains lots of theorems about circles).
*''Geometric Problems on Maxima and Minima'' - '''Titu Andreescu, Oleg Mushkarov, Luchezar Stoyanov''' - '''Problem''' book - '''Great''' book.
*''Complex Numbers in Geometry'' - '''I. M. Yaglom''' - '''Theory''' book.
*''Forum Geometricorum (A Journal on Classical Euclidean Geometry and Related Areas)'' - '''Authors''' - Uploaded by '''Amir Hossein Parvardi'''. ''AVAILABLE for DOWNLOAD''.
** [http://www.mediafire.com/download/v2rzcic8irni53r/Forum_Geometricorum_-_All_volumes.rar '''''All Volumes (direct link to the RAR file)'''''] - Alternative link: [http://s3.picofile.com/file/8211244900/Forum_Geometricorum_All_volumes.rar.html '''''All Volumes''''']



*[http://www.cip.ifi.lmu.de/%7Egrinberg/faq.html#books ''This''] note by [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=432 '''Darij Grinberg''']

*[http://sites.google.com/site/darijgrinberg/website '''''Darij Grinberg's''' whole site download''] - his [http://www.cip.ifi.lmu.de/~grinberg/ ''website''] has a great number of articles/solved problems that you may use in your Olympiad studying - '''Great'''.

*''Geometry revisited'' - '''Coxeter and Greitzer''' - '''Both''' book.

*''Problems in Geometry'' - '''Kutepov, Rubanov''' - '''Problem''' book.

*''Investigations in Geometry (Math Motivators!)'' - '''Posamentier, Sheridan''' - '''Both''' book.

*''Introduction to Geometry'' - '''Coxeter''' - '''Theory''' book.

*''Modern Geometry with Applications'' - '''Jennings''' - '''Both''' book.

*''Geometric Transformations (4 volumes)'' - '''Yaglom''' - '''Theory''' book.

==Combinatorics==
*''A Path to Combinatorics for Undergraduates'' - '''Andreescu, Feng'''.
*''Proofs that Really Count (The Art of Combinatorial Proof)''' - '''Benjamin and Quinn'''.
*''A Course in Combinatorics'' - '''Lint and Wilson'''.

==Improve Your Skills With Problem Solving==
===Algebra===
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=385236 ''100 Inequality Problems Proposed by Vasc and arqady''] - '''Amir Hossein Parvardi'''.
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=406530 ''115 Algebra Problems''] - '''Mohammad Jafari'''.
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=397768 ''100 Nice Polynomial Problems (With Solutions)''] - '''Amir Hossein Parvardi'''.
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=411461 ''100 Functional Equations Problems (With Solutions)''] - '''Amir Hossein Parvardi'''.
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=391940 ''Trigonometry Problems Collection''] - '''Amir Hossein Parvardi'''.
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=386343 ''567 Nice And Hard Inequalities''] - '''Nguyễn Duy Tùng'''.
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=398739 ''Inequalities From 2007 and 2008 Competitions Around The World''] - '''Manh Dung Nguyen'''.
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=398915 ''A Collection of Limits''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=61082 '''Pain rinnegan'''].
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=407914 ''Technical Analysis of Three Variable Inequalities''] - '''Nguyen Duy Tung, Zhou Yuan Zhe'''.

=== Number Theory ===

*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=492767 ''1220 Number Theory Problems (With Sources)''] - '''Amir Hossein Parvardi'''.
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=401494 ''Lifting the Exponent Lemma (LTE)''] - '''Amir Hossein Parvardi'''.
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=410293 ''Solving Diophantine Equations''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=94338 '''lamphong'''].
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=408084 ''Several Things About Sum of Squares''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=94338 '''lamphong'''].
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=399644 ''Some Own Problems In Number Theory''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=85314 '''mathmdmb'''].
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=399036 ''Primitive Roots, Order, and Quadratic Residues''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=85314 '''mathmdmb'''].
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=396930 ''Number Theory Marathon Problems''] - [http://www.artofproblemsolving.com/Forum/memberlist.php?mode=viewprofile&u=16383 '''M4RI0'''].

=== Geometry ===

*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=385682 ''150 Nice Geometry Problems (With Solutions)''] - '''Amir Hossein Parvardi'''.
*[http://sites.google.com/site/darijgrinberg/website '''''Darij Grinberg's''' whole site download''] - his [http://www.cip.ifi.lmu.de/~grinberg/ ''website''] has a great number of articles/solved problems that you may use in your Olympiad studying.
*
Euclidean Geometry in Mathematical Olympiads [http://web.evanchen.cc/geombook.html]

=== Combinatorics ===

*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=412125 ''100 Combinatorics Problems (With Sources)''] - '''Amir Hossein Parvardi'''.
*''102 Combinatorial Problems'' - '''Andreescu, Feng'''.
*''Problems in Combinatorics and Graph Theory'' - '''Ioan Tomescu'''.

=== General Problem Solving ===

*''Challenging Mathematical Problems With Elementary Solutions (Volume I, Combinatorial Analysis and Probability Theory)'' - '''A. M. Yaglom, I. M. Yaglom'''.
*''Challenging Mathematical Problems With Elementary Solutions (Volume II, Problem From Various Branches of Mathematics)'' - '''A. M. Yaglom, I. M. Yaglom'''.
*[http://www.artofproblemsolving.com/Forum/viewtopic.php?t=361972 '''''AoPS Resources Page Problems (IMO and ShortLists Added)'''''] - '''Amir Hossein Parvardi'''.
*''Mathematics as Problem Solving'' - '''Alexander Soifer'''.
*''A Primer For Mathematics Competitions'' - '''Alexander Zawaira, Gavin Hitchcock'''.
*''Problem Solving Strategies For Efficient And Elegant Solutions (A Resource For The Mathematics Teacher)'' - '''Alfred S. Posamentier, Stephen Kruli'''.
*''Problems for the Mathematical Olympiads (From the First Team Selection Test to the IMO)'' - '''Andrei Negut'''.
*''Problem Primer for the Olympiad'' - '''C. R. Pranesachar, B. J. Venkatachala, C. S. Yogananda'''.
*''Chinese Mathematics Competitions and Olympiads (two volumes)'' - '''Andy Liu'''.
*''Hungarian Problem Book''' ''(three volumes)'' - '''Andy Liu'''.
*''Canadian Mathematical Olympiad 1969-1993 (Problems and Solutions)'' - '''Michael Doob'''.
*''The Art and Craft of Problem Solving'' - '''Paul Zeitz'''.
*''APMO 1989-2009 ''(Problems & Solutions)'' - '''Dong Suugaku''' - [http://www.artofproblemsolving.com/Forum/download/file.php?id=33011 '''download here'''].
*''International Mathematical Olympiads 1978-1985 and Forty Supplementary Problems'' - '''Murray S. Klamkin'''.
*''USA Mathematical Olympiads 1972-1986 ''(Problems and Solutions)'' - '''Murray S. Klamkin'''.
*''USSR Mathematical Olympiads 1989-1992'' - '''Arkadii M. Slinko'''.
*''Proofs From THE BOOK'' - '''Martin Aigner, Günter M. Ziegler'''.
*''Techniques of Problem Solving'' - '''Steven G. Krantz'''.
*''Junior Balkan Mathematical Olympiads'' - '''Dan Branzei, loan Serdean, Vasile Serdean'''.
*''The IMO Compendium (A Collection of Problems Suggested for the Mathematical Olympiads, 1959-2004)'' - '''Dusan Djukic, Vladimir Jankovic, Ivan Matic, Nikola Petrovic'''.
*''Five Hundred Mathematical Challenges'' - '''Edward J. Barbeau, Murray S. Klamkin, William O. J. Moser'''.
*''The USSR Olympiad Problem Book (Selected Problems and Theorems of Elementary Mathematics)'' - '''D. O. Shklarsky, N. N. Chentzov, I. M. Yaglom'''.
*''The William Lowell Putnam Mathematical Competition (Problems and Solutions 1965-1984) (three volumes)'' - '''Volume 1''': '''A. M. Gleason, R. E'''. Greenwood, L. M. Kelly, '''Volume 2''': '''Gerald L. Alexanderson, Leonard F. Klosinski, Loren C. Larson''', '''Volume 3''': '''Kiran S. Kedlaya, Bjorn Poonen, Ravi Vakil'''.
*''International Mathematics TOURNAMENT OF THE TOWNS (Questions & Solutions)'' - (five volumes) - '''Peter J. Taylor'''.
*''Mathematical Problems and Proofs (Combinatorics, Number Theory and Geometry)'' - '''Branislav Kisacanin'''.
*''360 Problems for Mathematical Contests'' - '''Titu Andreescu, Dorin Andrica'''.
*''PROBLEMS FROM AROUND THE WORLD'' - (six volumes) - '''Titu Andreescu, Kiran S. Kedlaya, Paul Zeitz'''.
*''Mathematical Olympiad Treasures'' - '''Titu Andreescu, Bogdan Enescu'''.
*''Mathematical Olympiad Challenges'' - '''Titu Andreescu, Razvan Gelca'''.
*''Lecture Notes on Mathematical Olympiad Courses'' - '''Xu Jiagu'''.
*''Putnam and Beyond'' - '''Titu Andreescu, Razvan Gelca'''.
*''Hungary-Israeli Mathematics Competition'' - '''Shay Gueron'''.
*''MAA - The Contest Problem Book (Annual High School Contests)'' - (four volumes) - '''Volumes 1, 2, 3''': '''Charles T. Salkind, James M. Earl''', '''Volume 4''': '''Ralph A. Artino, Anthony M. Gaglione, Niel Shell'''.
*''Mathematical Olympiad in China (2007-2008) (Problems and Solutions)'' - '''Xiong Bin, Lee Peng Yee'''.
*''What to Solve (Problems and Suggestions For Young Mathematicians)'' - '''Judita Cofman'''.