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 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.
• Inequalities Theorems and Formulas forum.
• Useful Inequalities topic.

Polynomials

• Polynomials and Polynomial Inequalities (Graduate Texts in Mathematics) - (Springer) - Peter Borwein - Tamas Erdely.

• Geometry of Polynomials - (American Mathematical Society) - Morris Marden.

• Polynomials - (Springer) - E.J. Barbeau.
• Solving Polynomial Equations: Foundations, Algorithms, and Applications - (Springer) - Alicia Dickenstein - Ioannis Z. Emiris.

Functional Equations

• Functional Equations and Inequalities in Several Variables - (World Scientific Publication) - Stefan Czerwik.
• Lectures on Functional Equations - (Academic Press) - J. Aczel.
• Functional Equations: A Problem Solving Approach - (Prism Books) - B.J. Venkatchala.
• 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 - Problem 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.
• 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 - download here] - Theory Book.
• Numbers and Curves - Franz Lemmermeyer [free online - download here] - Theory Book.
• Algorithmic Number Theory - S. Arun-Kumar [free online - download here] - Theory Book.
• Elementary Number Theory - William Stein - [free online - 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 - download here].
• Geometry Unbound - Kedlaya - Theory book - this book is available online for download. See herel - 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.
• 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.
  • All Volumes

• This note by Darij Grinberg

• Darij Grinberg's whole site download - his 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

• 100 Inequality Problems Proposed by Vasc and arqady - Amir Hossein Parvardi.
• 115 Algebra Problems - Mohammad Jafari.
• 100 Nice Polynomial Problems (With Solutions) - Amir Hossein Parvardi.
• 100 Functional Equations Problems (With Solutions) - Amir Hossein Parvardi.
• Trigonometry Problems Collection - Amir Hossein Parvardi.
• 567 Nice And Hard Inequalities - Nguyễn Duy Tùng.
• Inequalities From 2007 and 2008 Competitions Around The World - Manh Dung Nguyen.
• A Collection of Limits - Pain rinnegan.
• Technical Analysis of Three Variable Inequalities - Nguyen Duy Tung, Zhou Yuan Zhe.

Number Theory

• 1220 Number Theory Problems (With Sources) - Amir Hossein Parvardi.
• Lifting the Exponent Lemma (LTE) - Amir Hossein Parvardi.
• Solving Diophantine Equations - lamphong.
• Several Things About Sum of Squares - lamphong.
• Some Own Problems In Number Theory - mathmdmb.
• Primitive Roots, Order, and Quadratic Residues - mathmdmb.
• Number Theory Marathon Problems - M4RI0.

Geometry

• 150 Nice Geometry Problems (With Solutions) - Amir Hossein Parvardi.
• Darij Grinberg's whole site download - his website has a great number of articles/solved problems that you may use in your Olympiad studying.

Combinatorics

• 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.
• 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 - 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.