Galois theory (pronounced "gal-wah") is a subject in mathematics that is centered around the connection between two mathematical structures, fields and groups. Fields are sets of numbers (sometimes abstractly called elements) that have a way of adding, subtracting, multiplying, and dividing. Groups are like fields, but with only one operation often called addition (subtraction is considered addition with negative numbers). Fields are often hard to study because there are so many possible combinations of numbers, that the internal structure is hard to decipher. Groups are usually much less complex and easier to understand. Galois theory gives a concrete connection between hard to study fields and easy to study groups.