From hybrid bicycle to MTB I have a 2013 Giant Escape 3. I intend to use it as an MTB or gravel bike. Please advise changes, if any, that I need to make to use the bike as an off road bicycle.
I intend to use it as an mtb or gravel bike


I assume you mean "MTB" as "cross-country", and I assume you do not plan to take part in competitions, except in those meant for absolute beginners.



The most important thing you could have done is to change tires to the widest the frame/fork would fit. However, this bike already comes with tires 35 mm wide, and I am afraid those are as big as one can squeeze there. You might want to change them  to ones with more "off-road" tread, but that would mean sacrificing the width, and I am not sure it is a reasonable trade off.

The next thing would be lowering the gear range available to you. Front of your bike has a triple with 28/38/48 teeth, and the rear cassette is 14-34 teeth. You are unlikely to ever use the front 48 teeth chainring offroad, while having a smaller smallest chainring is desirable; something like 22/34 at the front is what I typically use. Similarly, he rear cassette should have as big teeth count as possible, e.g. 11-36 or even 11-42 are likely to be achievable on the rear wheel hub you have now.

Changing gears as I described means you would have to change everything around them: rear and front cogs, rear and front derailleurs, rear and front shifters, the chain and possibly the cranks. Of course, you might be able to just find a bigger cassette or tighter front chainrings compatible with your existing system, but that is unlikely given that your drivetrain uses 7-speeds at the back.

The amount of changes I listed (+ installation costs) would cost you as much as a new bike. Your current bike is really just tuned for the city transportation task. 

So if you are serious about offroad riding, just go and sell the current bike and buy another one more suited for the task. Otherwise, just try riding your current bicycle where you want it; I'd say nothing prevents it to conquer regular gravel roads and easiest singletrack. Lower the tire pressure to have a bit of more cushion, swap in decent pedals to avoid feet slipping, take it slow, know your limits, and have fun!