Fifty Lectures for American Invitational Mathematics Examination (AIME) (Volume 1)

Lectures preparing for American Invitational Mathematics Examination (AIME) with plenty of problems with detailed solutions.
In the book, each chapter has three parts: (1) knowledge part talking about theorems, formulas, and skills with examples, (2) problems, (3) solutions to the problems.
Topics include:
Solid Geometry – Cube and Prism
Solid Geometry - Tetrahedron
Counting with Solid Geometry
Plane Geometry Similar Triangles
Plane Geometry Area and Area Method
Plane Geometry Menelaus and Ceva
Algebraic Manipulations
Logarithms
Solving Equations
Cauchy Inequalities