This compact treatment highlights the logic and simplicity of the mathematical structure of quantum mechanics. Suitable for advanced undergraduates and graduate students, it treats the language of quantum mechanics as expressed in the mathematics of linear operators. Originally oriented toward atomic physics, quantum mechanics became a basic language for solid-state, nuclear, and particle physics. Its grammar consists of the mathematics of linear operators, and with this text, students will find it easier to understand and use the language of physics. Topics include linear spaces and linear functionals; linear operators; diagonalizing operators; operator algebras; states; equations of motion; and representation of space-time transformations. The text concludes with exercises and applications.