A Banach space is a type of mathematical structure known as a vector space that is equipped with a norm. This norm allows for the measurement of the size or length of vectors within the space. A key feature of a Banach space is that it is complete, meaning that every Cauchy sequence of vectors in the space converges to a limit that is also within the space. Banach spaces are fundamental in functional analysis and have applications in various fields, including quantum mechanics and signal processing. Examples of Banach spaces include the space of continuous functions and the space of p-integrable functions, denoted as L^p spaces.