Math Olympiad

Books Recommendations:

Introductory Books:

• Dmitrii Vladimirovich Fomin, Ilia Itenberg, and Sergei Aleksandrovich Genkin - Mathematical Circles: Russian Experience (1996).

• M. R. Modak  S. A. Katre - An Excursion In Mathematics (2018).

Inequalities:

• Zdravko Cvetkovski - Inequalities Theorems, Techniques and Selected Problems (2012).

• B.J. Venkatachala - Inequalities: An Approach Through Problems (2009).

Functional Equations:

• Pang-Cheng, Wu - Functional Equation (2018). Link. 

Combinatorics:

• Titu Andreescu and Zuming Feng - A Path to Combinatorics for Undergraduates (2004).

• Pablo Soberón  - Problem-Solving Methods in Combinatorics An Approach to Olympiad Problems (2013).

• Chuan Chong Chen and Koh Khee Meng - Principles and Techniques in Combinatorics (1992).

• Daniel A Marcus - Combinatorics: A Problem Oriented Approach (1998).

Number Theory:

• Justin Stevens  - Olympiad Number Theory Through Challenging Problems (2016).

• David M. Burton - Elementary Number Theory (2010).

• Dorin Andrica and Titu Andreescu - Number Theory: Structures, Examples, and Problems (2009).

• Titu Andreescu, Gabriel Dospinescu, and Oleg Mushkarov - Number Theory: Concepts and Problems (2017).

• Ion Cucurezeanu, Dorin Andrica, Titu Andreescu - An introduction to Diophantine equations: A problem-based approach (2010).

• Michael Th. Rassias  - Problem-Solving and Selected Topics in Number Theory: In the Spirit of the Mathematical Olympiads (2010).

Geometry:

• Kiran S. Kedlaya - Geometry Unbound (2006).

• H. S. M. Coxeter, Samuel L. Greitzer - Geometry revisited (1996).

• Haibin Wang and Kim Hoo Hang - Solving Problems in Geometry: Insights and Strategies for mathematical olympiad (2018).

• Evan Chen - Euclidean Geometry in Mathematical Olympiads (2016).

Problem-Solving:

• Paul Zeitz - The art and craft of problem solving (2017).

• Derek Holton - A first step to Mathematical Olympiad problems (2010).

Links to Book Recommendations:

• A month for Olympiad-level geometry(MathStack) 

• Olympiad Combinatorics books(MathStack) 

• AOPS Olympiad Books recommendations 

• LIST OF BOOKS FOR MATH. OLYMPIADS (ISI, Bangalore) 

• Textbooks for math contests apart from AOPS(MathStack) 

Great resources(Links):

• Geometry Problems from IMOs 

• Olympiads - HBCSE - TIFR 

• Math Olympiad training handouts by Yufei Zhao 

• Olympiad Articles by Evan Chen 

• A Point of View. Dragomir Grozev's math blog. 

• A compiled version of IMO longlist Problems of previous years from 1959-2004.

• Some book pdfs are available here. 

•  Canadian Open Mathematics Challenge (COMC) 

• Berkeley Math Tournament 

• The USA Mathematical Talent Search (USAMTS) 

• Double Counting 

• An Introduction to Combinatorics and Graph Theory 

• Pigeonhole Principle 

• Carnegie Mellon Informatics and Mathematics Competition (CMIMC) 

• Ivy League Education Center 

• HMMT