In this talk I will introduce Grassmann (or anti-commuting) variables and the axioms of Grassmann-Berezin calculus. I will then show how we can use these Mathematical Physics tools to express Pfaffians and determinants and to derive various non-trivial identities such as the Lindstrom-Gessel-Viennot formula.   In the last part of the talk, I will define a one parameter extension of the skew Schur polynomial, an extension that obeys a natural convolution identity.