The equation $$f(x_1,\,x_2,\,...,\,x_m) = 0,$$ where the left hand side is a polynomial in $x_1$ $x_2$ ..., $x_m$ with coefficients in a certain field, is called an algebraic equation over that field. Often the field in question is $\mathbb{Q}$ then the coefficients may be assumed to be integers.

By the degree of an algebraic equation is meant the degree of the polynomial.

E.g. $3x^2-1 = 0$ , and $x^3+x^2y+xy^2+y^3 = 0$ , are algebraic equations over the field $\mathbb{Q}$ the degrees of which are 2 and 3.