The most important climbing gear!

The Rope
Climbing ropes are typically of kernmantle construction, consisting of a core (kern) of long twisted fibres and an outer sheath (mantle) of woven coloured fibres. The core provides about 80% of the tensile strength, while the sheath is a durable layer that protects the core and gives the rope desirable handling characteristics.
Carabiners
Carabiners are metal loops with spring-loaded gates (openings), used as connectors. Once made primarily from steel, almost all carabiners for recreational climbing are made from a light weight aluminum alloy. Steel carabiners are harder wearing, but much heavier and often used by instructors when working with groups.

Carabiners exist in various forms; the shape of the carabiner and the type of gate varies according to the use for which it is intended. There are two major varieties: locking and non-locking carabiners. Locking carabiners offer a method of preventing the gate from opening when in use. Locking carabiners are used for important connections, such as at the anchor point or a belay device. There are several different types of locking carabiners, including a twist-lock and a thread-lock.
Climbing Shoes
Specifically designed foot wear is usually worn for climbing. To increase the grip of the foot on a climbing wall or rock face due to friction, the shoe is covered with a vulcanized rubber layer. Usually, shoes are only a few millimetres thick and fit very snuggly around the foot. Stiffer shoes are used for "edging", more compliant ones for "smearing". Some have foam padding on the heel to make descents and rappels more comfortable. Climbing shoes can be re-soled which decreases the cost and environmental impact of purchasing new shoes.