Bessel's Inequality is a fundamental result in the field of functional analysis and signal processing. It states that for any sequence of vectors in a Hilbert space, the sum of the squares of the inner products of these vectors with any vector in the space is less than or equal to the square of the norm of that vector. This means that the projection of a vector onto a set of basis vectors cannot exceed the vector's total length. The inequality is particularly useful in applications like Fourier series and signal reconstruction, where it helps to understand how well a finite set of basis functions can approximate a given function. Bessel's Inequality ensures that even if the approximation is not perfect, it provides a bound on the error, making it a crucial tool in various mathematical and engineering disciplines.