This course will focus on the basic principles of the efficient congruencing method for estimating mean values of exponential sums. The course will cover the basic strategy for engineering a p-adic concentration argument, illustrated by confirmation of the main conjecture for moments in the first half of the critical range (diagonal estimates), and moments beyond twice the critical range (density estimates). Further topics include extensions to the multidimensional setting, the function field setting, and non-translation-invariant systems. This foundation will serve as a gateway into applications in number theory (Waring's problem), harmonic analysis (restriction theory) and arithmetic geometry (counting rational curves on varieties).