It totally depends where you gonna plan your trek? Monsoon is one of the most unpredictable weather in the mountains. Many risk factors do prevail like, landslides(which is very common), unexpected heavy downpour, risk of getting a infection is too common, and Snakes!!! I fear them a lot, especially in the jungle treks. But this weather is like an ornament that each and every mountains love to wear and monsoon makes mountains so beautiful. There will be clouds now and in the next moment there will be sunshine. Dense fog will engulf, tthe damp, swampy, misty fragrance will make things more alluring. So I'll suggest to visit some Hill station during the monsoon, and best time to trek is winters, snakes go into hibernation, and I love this fact so much.
Monsoon is a great time to trek in. I recently did the Valley of Flowers trek and the beauty of mountains is unmatched during monsoon. Obviously there will be threat of landslides, you'll just have to be a little cautious
Its absolutely adventure for you...just go and enjoy trekking experience... coz I hv my personal experience for 1st time trekking... just go with some group of people and bring with you some percussions like raincoat, trekking shoes it's very important for gripping and save you from the slipping ... !! :) try to visit vishapur for near pune ... check my profile I already uploaded some photos! :)
if you have any questions feel free to ask !