Because algorithmic traders acknowledge that their models are incorrectly specified we allow for ambiguity in their choices to make their models robust to misspecification. We show how to include misspecification to: (i) the arrival rate of market orders (MOs), (ii) the fill probability of limit orders, and (iii) the dynamics of the midprice of the asset they trade. In the context of market making, we demonstrate that market makers (MMs) adjust their quotes to reduce inventory risk and adverse selection costs. Moreover, robust market making increases the strategy's Sharpe ratio and allows the MM to fine tune the tradeoff between the mean and the standard deviation of profits. Our framework adopts a robust optimal control approach and we provide existence and uniqueness results for the robust optimal strategies as well as a verification theorem. The behavior of the ambiguity averse MM generalizes that of a risk averse MM, and coincide in only one circumstance.