Thanks, Vihart of YouTube!
In this video, elementary algebra is built up from counting to positive numbers to negative numbers to multiplication and division to exponents and logarithms. All these concepts are tied together under the common theme of "fancy counting." That is, each of these operations is tied directly to the fundamental operation of "+1".
All of this in just over 9 minutes. This is how experts think of algebra. Novices, new to the world of algebra, see the mechanical steps to be taken, the shuffling of symbols, the confusing mass of numbers, letters, and symbols and get lost. Experts think of algebra as chunks of value that are being operated upon by a (relatively) small set of operations, made smaller by lumping an operation with its inverse (addition/subtraction, multiplication/division, exponents/logarithms) and realizing they are two sides of the same coin.