This chapter introduces seminal quantum algorithms that illustrate quantum computation’s efficiency over classical methods. The Deutsch and Deutsch–Jozsa algorithms showcase quantum parallelism, offering solutions to specific problems with fewer computational steps. The quantum Fourier transform (QFT) is introduced, underpinning period-finding algorithms as well as Shor’s algorithm for integer factorization, which has major implications for cryptography. Grover’s algorithm demonstrates a quadratic speedup for unstructured search problems. By using superposition, entanglement, and phase manipulation, these algorithms highlight the computational power of quantum mechanics and its potential to outperform classical techniques, particularly for complex or classically intractable tasks.