A lathe comprising: a main spindle which grips such that a centerline of a work becomes horizontal and rotates the work so that the centerline of the work becomes an axis of rotation, and is reciprocatable in a Z direction which is parallel with aft the axis of rotation of the work; a back spindle which is positioned oppositely to the main spindle, grips and rotates a work, and is reciprocatable in the Z direction; a tool spindle which has a tool for machining the work attached thereto such that a centerline of the tool becomes horizontal, wherein the tool spindle is reciprocatable in the Z direction (Z2-axis direction) and also reciprocatable in the X direction (X1-axis direction) that is a horizontal direction different from the Z direction; wherein the main spindle comprises a hole through which the work penetrates, so that the work can be gripped by the main spindle and can extend by penetrating through the hole; a guide bush which rotatably supports the work projecting from the main spindle, and slides the work in a direction of axis of rotation of the work; the lathe characterized by comprising a tool magazine which contains a plurality of tools; and a tool exchange mechanism which exchanges the attached tool to a tool contained in the tool magazine; wherein the back spindle comprises a hole through which the work penetrates, so that the work can be gripped by the back spindle and can extend by penetrating through the hole; and the lathe further characterized in that the tool spindle rotates in an X - Z plane including the Z direction and the X direction to change a direction of the tool, and in that the tool spindle is also reciprocatable in a Y direction which is different from the Z and X directions. a main spindle which grips such that a centerline of a work becomes horizontal and rotates the work so that the centerline of the work becomes an axis of rotation, and is reciprocatable in a Z direction which is parallel with aft the axis of rotation of the work; a back spindle which is positioned oppositely to the main spindle, grips and rotates a work, and is reciprocatable in the Z direction; a tool spindle which has a tool for machining the work attached thereto such that a centerline of the tool becomes horizontal, wherein the tool spindle is reciprocatable in the Z direction (Z2-axis direction) and also reciprocatable in the X direction (X1-axis direction) that is a horizontal direction different from the Z direction; wherein the main spindle comprises a hole through which the work penetrates, so that the work can be gripped by the main spindle and can extend by penetrating through the hole; a guide bush which rotatably supports the work projecting from the main spindle, and slides the work in a direction of axis of rotation of the work; the lathe characterized by comprising a tool magazine which contains a plurality of tools; and a tool exchange mechanism which exchanges the attached tool to a tool contained in the tool magazine; wherein the back spindle comprises a hole through which the work penetrates, so that the work can be gripped by the back spindle and can extend by penetrating through the hole; and the lathe further characterized in that the tool spindle rotates in an X - Z plane including the Z direction and the X direction to change a direction of the tool, and in that the tool spindle tool magazine which contains a plurality of tools; and a tool exchange mechanism which exchanges the attached tool to a tool contained in the tool magazine; wherein the back spindle comprises a hole through which the work penetrates, so that the work can be gripped by the back spindle and can extend by penetrating through the hole; and the lathe further characterized in that the tool spindle rotates in an X - Z plane including the Z direction and the X direction to change a direction of the tool, and in that the tool spindle