Top roping is a style in climbing in which a rope, used for the climber’s safety, runs from a belayer at the foot of a route through one or more carabiners connected to an anchor system at the top of the route and back down to the climber.
Bouldering is climbing on short, low routes, without the use of the safety rope that is typical of most other styles. Protection typically consists of a cushioned bouldering pad below the route and/or a spotter (a person who watches from below and tries to break hazardous falls for the climber.)
Lead Climbing is climbing without the use of pre-set belays. One person (the leader) will start the climb carrying one end of the rope and will gradually attach it to additional anchors as he/she climbs, thereby establishing a belay system that progresses with the climb.