This book is intended for university and technological institute students and contains the material of the Analytical Geometry course.

In the first chapter (Vector Calculus), the concept of the vector, coordinates in the plane and space, various vector products, and the change of coordinate systems are introduced.

In the second chapter (Analytical Geometry of the plane), the known lines of the plane are presented, including the straight line, the circle, the parabola, the ellipse, and the hyperbola.

In the third chapter (The plane in space), a brief reference is made to the basic knowledge of Stereometry that a student should possess, followed by a detailed presentation of various cases for finding the equation of a plane with the relevant properties.

In the fourth chapter (The line in space), an in-depth study of the different forms of the equation of a line in space, the relative positions of lines and planes, the common perpendiculars of skew lines, and the distance from a point to a line is undertaken.

In the fifth chapter (The sphere), the relevant concepts associated with the sphere in space are presented.

In the sixth and final chapter (Surfaces of the second degree), cylindrical surfaces, conic surfaces, and surfaces of revolution are discussed. Additionally, a classification of surfaces of the second degree is provided.

In each chapter, numerous examples are solved for the understanding of all the concepts developed. Furthermore, representative exercises are included, which are summarized at the end of the book.

Finally, the book contains an index of terms covering all the concepts of Analytical Geometry.