ACROSS
3. A person who climbs mountains, a mountain climber →
mountaineer
4. Illness caused by ascent to high altitude, characterized by hyperventilation, nausea, and exhaustion resulting from shortage of oxygen →
altitudesickness
5. The pointed top of a mountain →
peak
6. A camp from which mountaineering expeditions set out →
basecamp
7. A tool consisting of a shaft, grip, strap, etc., used to reduce the burden on the lower body and maintain balance when climbing→
stick

DOWN
1. A covering for the hand that has separate parts for each finger →
glove
2. A type of flashlight/equipment designed to be worn on the head and fixed to the head →
headlantern
3. A building located at high elevation, in mountainous terrain, generally accessible only on foot, intended to provide food and shelter for mountaineers, climbers and hikers →
mountainhut
8. A set of outdoor activities that involves ascending mountains →
 climbing