The work provides an introduction to linear algebra and analytical geometry and includes material for a two-semester lecture. It begins with a chapter that introduces the mathematical way of thinking and proof techniques, before transitioning to linear algebra through systems of linear equations. Special emphasis is placed on a close interconnection between algebraic and geometric concepts, both to develop a strong geometric intuition for algebraic terms and to apply elegant algebraic proof methods to geometric theorems. The text is written clearly and understandably, in a refreshing style. Finally, interactive exercise pages and illustrations are integrated to encourage active study.