This course covers selected topics in Quantum Computing with a view toward Quantum Cryptography. The course consists of two parts. Part I begins with a review of linear algebra basics and a detailed exploration of the four postulates of quantum mechanics, including an alternative formulation using density operators. The course then progresses to core concepts like qubits, the quantum circuit model, and then reviews various quantum algorithms such as the quantum Fourier transform and phase estimation. In Part II, the focus shifts to Quantum Cryptography, covering Quantum Key Distribution. The remaining portion of the course explores public-key quantum cryptography, focusing on topics like Quantum Money and Quantum public-key encryption.