Textbooks for math contests apart from AoPs I am looking for textbooks on math contests that give the theory associated with the topics
(such as graph theory,geometry,Trig,combinatorics,etc) before giving a large volley of problems to solve(apart from AoPs). I am a high schooler and  complete beginner to these.
Is there a textbook that discusses theory as good as Arthur Engel has done for problem solving in the book Problem Solving Strategies?
 A: Here are the books I recommend every mathlete from my personal experience:
Geometry and Trigonometry:

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*Euclidean Geometry in Mathematical Olympiads by Evan Chen: This is the most recommended book for Olympiad geometry. The book goes through many important concepts and also gives insights of solving problems.

*Geometry Revisited by H.S.M Coxeter: An awesome classic. Some IMO medalists still recommend this book above EGMO.

*Geometry Unbound by Kiran S. Kedlaya: If you've completed all necessary concepts in geometry and want to solve some good problems, this is the book you're looking for.

*103 Trigonometry Problems by Titu Andreescu: A good problem book for Olympiad trigonometry.

Inequalities:

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*Secrets in Inequalities volume 1 and 2 by Pham Kim Hung: The best inequality book. But not recommended for a complete beginner as the problems here are very high level.

*Inequalities a Mathematical Olympiad Approach by Rogelio: A good book for Olympiad inequalities. Also suitable for beginners.

*Inequalities- Theorems, Techniques and Selected Problems by Cvetcovski (suggested by Dr. Mathva)

*Inequalities an Approach Through Problems by B J Venkatachala

Functional Equations:

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*Functional Equations and How to Solve Them by Christopher G. Small

*Functional Equations a Problem Solving Approach by B J Venkatachala

Algebra:

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*101 Problems in Algebra by Titu Andreescu

Number Theory:

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*Modern Olympiad Number Theory by Aditya Khurmi (suggested by Dr. Mathva)


*Olympiad Number Theory Through Challenging Problems by Justin Stevens


*Number Theory a Problem Solving Approach by Titu Andreescu


*104 Number Theory Problems by Titu Andreescu
Combinatorics:

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*A Path to Combinatorics for Undergraduates by Titu Andreescu

*102 Combinatorial Problems by Titu Andreescu

*Problem Solving Methods in Combinatorics by Pablo Soberón

*Graph Theory by Xiong Bin

Problem Solving:

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*The Arts and Crafts of Problem Solving by Paul Zeitz: The best problem solving book. Also a good resource for recreational mathematics problems.

*How to Solve It by George Polya.

Again, I mention these are my recommendations. Others suggestion may differ from this (you may add your suggestions in the comments). And there might be some books I forgot to include. May your math journey be enjoyable. Happy problem solving!
