Cut the ginger into thin slices, then coarsely chop it into smaller pieces.
Place the ginger along with the water, sugar, and salt in a non-reactive saucepan. Bring to a boil, then reduce the heat to a steady simmer. Cook for 45 minutes to one hour.
Let cool, then strain the syrup through a fine-mesh strainer. Store the strained syrup in the refrigerator, covered, until ready to use.
TO MAKE GINGER ALE: Fill glasses with ice, the pour ginger syrup to ¼-⅓ of the glass (depending on your taste), add a generous squeeze of fresh lemon or lime juice. Top with sparkling water or tonic water. Stir gently to mix the ingredients and garnish with a round of citrus or fresh mint.
