When I was a boy I sometimes climbed with my brother, a. As a child it was a very exciting experience but I never did it as a leader.

I think this deserves splitting into two sentences. The second sentence may require a comma somewhere so please don't accept it as gospel.

Many years afterwards I met a colleague that was going to climb, and after chatting, I began going with him.

This makes it sound like your colleague was not a regular climber when you were chatting or that he was just about to go for a climbing session.

At the beginning we went to an indoors gym, wthat iwas called "bouldering", but after a few months we started to go outdoors and climbed with ropes.

I like the way that climbing teaches you how to really focus, especially when you're the climb leader, otherwise you get paralized by fear.

Among all the types of climb I prefer rock climbing, mainly multi-pitch routes, because it's indeed a team sport indeed.

My correction makes it sound rather Victorian. I would personally use 'certainly' instead of indeed

After 6 years I still work with that guy and nowadays we aren't onlyjust colleagues we are climb partners.