A sliding table assembly for a main table of a table saw, the sliding table assembly, comprising: a) a sliding table member including at least one longitudinally extending rail structure; b) a bracket structure configured to be attached to a mounting structure on the main table of the table saw, the bracket structure including: b1) a first bracket member arranged facing in a first direction and configured to be positioned in engagement with a first lateral surface of the at least one rail structure; and b2) a second bracket member arranged facing in a second direction that is opposite the first direction and configured to be positioned in engagement with a second lateral surface of the at least one rail structure; c) a vertical position adjustment mechanism operably connected to the bracket structure and configured to move at least a portion of the bracket structure vertically with respect to the mounting structure; and d) a horizontal position adjustment mechanism operably connected to the bracket structure and configured to move at least a portion of the bracket structure horizontally with respect to the mounting structure; e) wherein at least one of the first bracket member and the second bracket member comprises a movable bracket member that is configured to move with respect to the other bracket member such that the first bracket member and the second bracket member are each pressed against the first lateral surface and the second lateral surface, respectively, to slidably retain the at least one rail structure in the bracket structure, and f) wherein the movable bracket member includes a fastener structure that is configured to releasably secure the movable bracket member in position with the at least one rail structure slidably retained in the bracket structure. a) a sliding table member including at least one longitudinally extending rail structure; b) a bracket structure configured to be attached to a mounting structure on the main table of the table saw, the bracket structure including: b1) a first bracket member arranged facing in a first direction and configured to be positioned in engagement with a first lateral surface of the at least one rail structure; and b2) a second bracket member arranged facing in a second direction that is opposite the first direction and configured to be positioned in engagement with a second lateral surface of the at least one rail structure; b1) a first bracket member arranged facing in a first direction and configured to be positioned in engagement with a first lateral surface of the at least one rail structure; and b2) a second bracket member arranged facing in a second direction that is opposite the first direction and configured to be positioned in engagement with a second lateral surface of the at least one rail structure; c) a vertical position adjustment mechanism operably connected to the bracket structure and configured to move at least a portion of the bracket structure vertically with respect to the mounting structure; and d) a horizontal position adjustment mechanism operably connected to the bracket structure and configured to move at least a portion of the bracket structure horizontally with respect to the mounting structure; e) wherein at least one of the first bracket member and the second bracket member comprises a movable bracket member that is configured to move with respect to the other bracket member such that the first bracket member and the second bracket member are each pressed against the first lateral surface and the second lateral surface, respectively, to slidably retain the at least one rail structure in the bracket structure, and f) wherein the movable bracket member includes a fastener structure that is configured to releasably secure the movable bracket member in position with the at least one rail structure slidably retained in the bracket structure.