This book is addressed to students of the 2nd grade of the Lyceum (Positive direction), but also to fellow Mathematicians (given that it includes a large and original collection of exercises). It is written based on the new syllabus provided for this class. It includes seven chapters that refer to vectors , the line , the circle , the parabola , the ellipse , the hyperbola and conic sections , in general. At the end of each chapter there are approximately fifty solved exercises, while a special appendix contains solved general application problems of the respective theory.

Emphasis is placed on exercises unknown in the Greek literature and on subjects of various exams and competitions (French Baccalaureate , exams of the Universities of Cambridge , London , Oxford , Moscow , Bucharest , etc., G. Putnam competition, Olympiad competitions, E.M.E competitions etc. ) .

An effort was made for an understandable presentation of the relevant theory, for a methodological confrontation of certain issues and for a perfect collection of exercises, the degree of difficulty of which is marked with one, two or three asterisks.