Mathematics has so many divisions, but you do not have to be
expert in all parts for Mathematical Olympiads. If you check the past papers of
any Mathematical Olympiad, especially International Mathematical Olympiad, then
you’ll see that it basically covers **Number
Theory, Algebra, Geometry, Combinatorics and Inequality**. To solve the
problems you’ve to increase your problem solving skills, know some tricks and enhance
the capability of doing problems using the best method.

I’m giving you some book suggestion to start your preparation
for Mathematical Olympiad. Books are given in order of difficulty. So, if you
are a beginner, you should start with the first book of each part.

__Number
theory__

(i) Beginning Number Theory

(ii) Number Theory

(iii) Adler’s Number Theory

(iv) A Pathway into Number Theory

(v) Elementary Number Theory

(vi) A Primer of Analytic Number Theory

__Algebra__

(i)
Concrete Abstract Algebra

__Geometry__

(i)
Plane Euclidean Geometry Theory & Problems

(ii) Geometry Revisited

(iii) Geometry Unbound

(iv) Complex number & Geometry

(v) The Algebra of Geometry

(vi) Transformation Geometry

__Combinatorics__

(i) Combinatorics

(ii) Principles and Techniques in Combinatorics

(iii) A Path to Combinatorics for Undergraduates

__Inequality__

(i) Inequalities

(ii) Algebra Inequalities

(iii) Secrets in Inequality