How many covalent bonds can one atom of carbon form?

A carbon atom can form 4 single covalent bonds

Carbon Atoms Can Form Four Single Bonds OR Two Double Bonds.

Because its outer shell can hold up to eight electrons, carbon can share electrons with up to four other atoms. Therefore, it can from four covalent bonds.

4 at the most without it being unstable

Since a carbon atom has four valence electrons, it can bond with a maximum of four atoms, (e.g. methane or CH4).