Start a new Activity from Fragment

If you have a look at the documentation you can see that to start an activity you'll want to use the following code

Intent intent = new Intent(getActivity(), AnotherActivity.class);
startActivity(intent);

Currently you're using MainActivity.class in a place that requires a context object. If you're currently in an activity, just passing this is enough. A fragment can get the activity via the getActivity() function.

Your full code above should look like this

Button button = (Button) rootView.findViewById(R.id.button1);
button.setOnClickListener(new View.OnClickListener() {
    @Override
    public void onClick(View view) {
        Intent intent = new Intent(getActivity(), AnotherActivity.class);
        startActivity(intent);
    }
});

Button button = (Button) view.findViewById(R.id.button_ID);
button.setOnClickListener(new View.OnClickListener() {
    @Override
    public void onClick(View view) {
        Intent myintent = new Intent(getActivity(), CallingActivity.class);
        startActivity(myintent);
    }
});

If you have to use it inside onBindViewHolder, you may do this:

@Override
public void onClick(View view) {
    Intent intent= new Intent(view.getContext(), MainActivity.class);
    view.getContext().startActivity(intent);
}

You should use getActivity() to launch an Activity from Fragment.

From a Fragment: Context is parent activity (getActivity()).

Intent intent = new Intent(getActivity(), AnotherActivity.class);
startActivity(intent);