The Riemann Hypothesis is the statement that the non-trivial zeroes of the Riemann zeta function lie on the critical line $\Re(s) = 1/2$. In this paper, we establish the Riemann Hypothesis. The proof relies primarily on the following ingredients: a new Fourier-analytic representation for the Riemann zeta function, the explicit formula connecting the zeroes of the zeta function with the primes, the structure theory of multiplicative functions, the Matomaki-Radziwi\l\l theorem, and a new multilinear sieve method for estimating correlations of multiplicative functions.

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