"$\backslash$" notation question in definition for Nash equilibrium
Informally, a (possibly mixed) set of strategy choices is a Nash equilibrium if no player can expect to benefit by changing strategies while the other players keep their strategies unchanged. 

Here I would interpret your definition as $\Delta$ being the set of all possible strategy choices across all players, $\sigma^*$ being a set of strategy choices which will be a Nash equilibrium if it satisfies the conditions, $i$ being a player, and $\sigma^* \backslash \mu_i$ being a change in player $i$'s strategy while the other players' strategies stay the same.  So I would take $\backslash$ having a type of "not included" interpretation.