The manual consists of three sections. The first section outlines an algebraic approach to solving a large class of triangle geometry problems. In particular, some general method has been proposed to prove a certain type of geometric inequality. The second section deals with the presentation of both classical results and recently published results (mainly in the journal "Forum Geometricorum") on quadrilateral geometry. The third section contains a number of tasks for self-solution, many of which are accompanied by detailed instructions. The manual is intended for high school students, secondary school teachers, as well as students and teachers of mathematics departments of higher educational institutions.