This course provides a rigorous mathematical introduction to quantum algorithms and post-quantum cryptography, focusing on theoretical foundations rather than physical realizations. It covers Hilbert spaces, unitary transformations, quantum gates, and computational complexity theory. The course emphasizes algorithmic aspects, including Deutsch’s algorithm, Simon’s algorithm, Grover’s search, and Shor’s factorization algorithm, with a strong algebraic and complexity-theoretic approach. The final four weeks introduce post-quantum cryptography from a mathematical perspective, covering code-based and lattice-based cryptographic techniques that ensure security in a quantum computing era. Graduate students will engage with additional research-based assignments and theoretical proofs.