Pell's Equation is a type of Diophantine equation of the form x^2 - Ny^2 = 1, where N is a non-square integer, and its solutions are of great interest in number theory due to their connection with continued fractions and quadratic forms. The equation is named after John Pell, although it was first studied by Indian mathematicians like Brahmagupta and later by European mathematicians such as Euler and Lagrange, who developed methods to find its integer solutions.