Quantum Computing (QC) has witnessed remarkable growth and has garnered significant attention in recent years, often accompanied by strong hype. This introductory talk aims to provide a comprehensive overview of the fundamental concepts in QC and its potential for Mathematicians. The talk begins by explaining the core principles of QC like entanglement and superposition. Furthermore, the talk delves into the mathematical underpinnings of QC, demonstrating how operations on a quantum computer can be elegantly described using linear algebra. This approach enables the manipulation and analysis of quantum states, paving the way for the development of quantum algorithms. As an illustration of the power of quantum computing, the concept of quantum teleportation will be introduced, showcasing the remarkable ability to transmit quantum information using classical channels. The talk also highlights two influential quantum algorithms: Shor's and Grover's algorithm. Shor's algorithm, renowned for its impact on cryptography, presents a polylogarithmic approach to factoring large numbers, thereby threatening conventional encryption methods. On the other hand, Grover's algorithm offers a powerful tool for database search, potentially providing a quadratic speedup compared to classical search algorithms. Lastly, the current state of the art in quantum computing is addressed.