  These notes rigorously construct the stochastic integral of a Hilbert Space
valued process driven by a Cylindrical Brownian Motion. We expand upon this
stochastic calculus to present an introduction to stochastic differential
equations in infinite dimensions, with a particular focus on Stratonovich
equations due to their physical importance as well as unbounded noise operators
(with applications to transport noise). Furthermore we explore techniques in
the existence theory for nonlinear stochastic partial differential equations.
