Study everything - that's your best bet. Important subjects probably include: Polynomials, Exponents, Radicals, Solving Equations, Solving Inequalities, Absolute Value Equations and Inequalities, Lines, Word Problems, Systems of Equations (2x2's), Factoring, Division of Polynomials, Quadratics, Parabolas, Complex Numbers, Algebraic Fractions, Functions
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The study of algebra is commonly referred to as arithmetic. This is a branch of mathematics which is a broad science.
There are no types of algebra which are their algebra. If you study and master them, they become yours.