An introductory path to quantum theory : using mathematics to understand the ideas of physics Introduction to this Path Viewpoint Neither Particle nor Wave Schrödingers Equation Operators and Canonical Quantization The Harmonic Oscillator Interpreting: Mathematics Interpreting: Physics The Language of Hilbert Space Interpreting: Measurement The Hydrogen Atom Angular Momentum The Rotation Group SO(3) Spin and SU(2) Bosons and Fermions Classical and Quantum Probability The Heisenberg Picture Uncertainty (Optional) Speaking of Quantum Theory (Optional) Complementarity (Optional) Axioms (Optional) And Gravity Measure Theory: A Crash Course. Since the 17th century physical theories have been expressed in the language of mathematical equations. This introduction to quantum theory uses that language to enable the reader to comprehend the notoriously non intuitive ideas of quantum physics. The mathematical knowledge needed for using this book comes from standard undergraduate mathematics courses and is described in detail in the section Prerequisites. This text is especially aimed at advanced undergraduate and graduate students of mathematics computer science engineering and chemistry among other disciplines provided they have the math background even though lacking preparation in physics. In fact no previous formal study of physics is assumed.