Let $R=\mathcal{C}([0,1],\mathbb{R})$ be the ring (standard one) of continuous functions. For each $\gamma\in[0,1]$, let $I_\gamma=\{f\in R; f(\gamma)=0\}$. It is easy to prove that $I_\gamma$ is an ideal, in fact, a maximal one.
My question is: how to find other ideals (not necessarily maximal), that is, different of the type of $I_\gamma$?