Abstract: The Algebraic Envelope over a commutative ring R is the initial object in the category of affine R-algebra schemes. Algebraic envelopes are important because they contain a lot of data about general affine R-algebra schemes. Unfortunately, an explicit characterization of these objects remains elusive. We will see that these objects can be understood in terms of the multiplicative and unipotent parts of the underlying additive group scheme when we are over a field of characteristic zero. Time permitting, we will also see some examples.