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Geometric algebra is a versatile and powerful mathematical framework that combines the strengths of geometry, algebra, and calculus. It has the potential to revolutionize the way we approach and solve a wide range of problems across various disciplines.
There are multiple ways to study geometric algebra (GA). This wiki primarily focuses on learning GA through practical applications.
On a very general level, each of the geometric primitives (spheres, circles, planes, lines, points) can be expressed by the same mathematical unit -- a multivector. For simplicity, although at the risk of sounding non-academic, the term 'multivector' can be expressed as a special "multidimensional vector." Different components of multivectors have different rules for mathematical operations over them. Collectively, these rules make up the geometric algebra.