Step 1: Definition of molarity.
Molarity (M) = $\dfrac{\text{Number of moles of solute}}{\text{Volume of solution in litres}}$.
Step 2: Find moles of water.
- Molar mass of water = 18 g mol$^{-1}$.
- Density of water = 1000 g L$^{-1}$.
So, number of moles in 1 L of water = $\dfrac{1000}{18} = 55.56$ mol.
Step 3: Conclusion.
Thus, the molarity of pure water is 55.56 mol L$^{-1}$.
Final Answer:
\[
\boxed{55.56 \ \text{mol L}^{-1}}
\]