Suppose $n$ is a big number and $k\geq 2$. How many sets $S_1,\dots,S_m\subset [n]$ can we find such that (1) $|S_i| = k$ for all $i$, (2) $|S_i\cap S_j| \leq 1$ for all $i\ne j$. What's the maximum possible value of $m$?

(I just need to know the growth order of $m$ depending on $n$ and $k$. For instance, when $k=2$, we have $m = \binom{n}{2} \sim n^2$.)

I tried to look it up in the literature, but it looks like this is different from the classical intersecting family that I have an upper bound on the size of intersection of a pair of sets instead of a lower bound.