General Problem Solving:

 "Problems in Mathematics" by Arthur Engel

 "Problem Books in Mathematics" by Loren C. Larson  

Booklist

Inequality:

"Inequalities A Mathematical Olympiad Approach" by Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado   
"Basics of Olympiad Inequalities" by Samin Riasat

Number Theory:

"Number Theory for Mathematical Contests" by David A. SANTOS

"104 Number Theory Problems From the Training of the USA IMO Team" by Birkhauser

"Olympiad Number Theory Through Challenging Problems" Justin Stevens

"NUMBER THEORY Structures, Examples, and Problems" by Titu Andreescu Dorin Andrica

Combinatorics:

"Enumerative Combinatorics Through Guided Discovery" by Kenneth P. Bogart

"Olympiad Combinatorics" by Pranav A. Sriram

"102-Combinatorial-Problems-2002" by Titu Andreescu, Zuming Feng

Geometry:

"Lemmas In Olympiad Geometry" by Navneel Singhal

"Geometry" by Alexander Remorov

"GEOMETRY REVISITED" by H. S. M. Coxeter

General:

"Lecture Notes on Mathematical Olympiad" by Xu Jiagu

Algebra:

"101 PROBLEMS IN ALGEBRA FROM THE TRAINING OF THE USA IMO TEAM" by Titu Andreescu, Zuming Feng