Wash the currants and remove them from their stems.*
Sterilize your canning jars.
While the jars are sterilizing, put the red currants and water in a large, non-reactive pot (no cast iron unless it is enameled, and no aluminum). Gently crush the currants with a potato masher or the bottom of a wine bottle. Add the sugar. Cook the mixture over medium-low heat, stirring constantly to dissolve the sugar.
Once the sugar is completely dissolved, raise the heat to high and boil, stirring often, until the jam reaches the gel point. Remove the red currant jam from the heat and skim off any foam that has formed on the surface.
If the jam reaches the gel point before the jars are sterilized, simply remove the jam from the heat until the jars are ready. Reheat the jam just barely back to a simmer before filling the jars.
Ladle the hot jam into the sterilized jars leaving 1/4 to 1/2-inch headspace. Screw on canning lids. You can simply allow the jars to cool and then store them in the refrigerator for up to 3 months. For longer-term storage at room temperature, process the jars in a boiling water bath for 5 minutes.