I'm reading Landman/Robertson's: Ramsey Theory on the Integers. It states the following theorem:
Theorem 1.15 (Ramsey's Theorem for Two Colors). Let $k,l \geq 2$. There exists a least positive integer $R=R(k,l)$ such that every edge-coloring of $K_R$, with the colors red and blue, admits either a red $K_k$ subgraph or a blue $K_l$ subgraph.
But It's not clear what $R(k,l)$ is.
They're actually defining $R(k, l)$ in the statement of that theorem. It would probably have been more evident if they said something like:
Theorem 1.15: Let $k,l\geq 2$. There exists a least positive integer $R$ such that every edge-coloring of $K_R$, with the colors red and blue, admits either a red $K_k$ subgraph or a blue $K_l$ subgraph.
Note: The integer $R$ guaranteed by Theorem 1.15 is denoted $R(k, l)$.