An introduction to Witt vectors

In this talk, we introduce the construction of the ring $W(R)$ of Witt vectors over a commutative unitary ring $R$. Following the construction of $W(R)$, we pause to explore the ring structure in order to develop familiarity with the ring operations, and we also discuss various useful maps that can be defined on $W(R)$. Afterwards, we specialize exclusively to the case $R={\mathbb{F}}_p$, the finite field with $p$ elements, and obtain an isomorphism $W(F_p) \cong {\mathbb{Z}}_p$, the ring of $p$-adic integers.