This four-color textbook is aimed at students of mathematics, physics, and computer science in bachelor's and teaching degree programs. It provides a vivid picture of linear algebra as it is typically covered in the first year of study. Students of mathematics and related fields will find important concepts, theorems, and proofs explained in detail with many examples, and will be introduced to fundamental concepts and methods.

The focus is on understanding mathematical relationships and the structure of the theory, as well as the structures and ideas of important theorems and proofs. It not only presents a coherent theoretical framework but also illustrates how it is developed and what the content will be used for later.

Outstanding features include:

• Consistently four-color layout
• More than 150 illustrations
• Concisely formulated core ideas serve as section headings
• Detailed exercise examples encourage 'learning by doing'
• Self-tests at short intervals allow for learning checks while reading
• Colored highlight boxes emphasize the most important points
• 'Background-and-Outlook' boxes establish connections to other areas and advanced topics
• Overview boxes summarize important results
• More than 250 comprehension questions, calculation tasks, and proof exercises

This book will be a reliable companion for all students of mathematics and related fields from the beginning of their studies through to higher semesters.

The content of this book is largely based on the work 'Fundamental Knowledge for Mathematics Studies - Analysis and Linear Algebra with Cross-Connections', but is published here in a completely revised form as an independent work due to its curricular significance.