Algebraic geometry occupies a central place in modern mathematics. The concepts it uses connects it to such diverse fields as complex analysis, topology and number theory. At the start, algebraic geometry was about studying systems of polynomial equations in several variables. Algebraic geometry starts at the point where equation solving leaves off: In many cases, finding the properties all the solutions a given set of equations have is more important than finding a particular solution: this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.