The Fourier transform, named after Joseph Fourier, is a mathematical transform with many applications in physics and engineering. Very commonly it transforms a mathematical function of time, f(t), into a new function, sometimes denoted by or F, whose argument is frequency with units of cycles or radians per second. The new function is then known as the Fourier transform and/or the frequency spectrum of the function f. [Source: Wikipedia]

[Source: **SMBC**]

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TL;DR

Fourier transform allows you to convert a signal from space/time domain (picture, song, etc.) into frequency domain (let you see different frequencies and their strength)

Useful application: Let you separate a complex signal into simple sin/cos signals, able to filter certain frequency (to get rid of noise and pick up human voice), construct MRI picture, solve “complex” equations etc.

PS Fourier and LaPlace are very similar, but the limit of the integral are different in both cases.

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