Make Simple Syrup: Combine water and sugar in a small saucepan. Over medium heat, stir until sugar is fully dissolved and a syrup-like liquid forms. Remove from heat and let cool for 5 minutes.
Mix Cocktail: Half-fill a shaker with ice. Add the simple syrup, gin and lime juice. Shake vigorously for 1-2 minutes. Strain into glass. Attach lime slices to edge of glasses. Serve.