Cannot resolve method startActivity()

You should use the context of your adapter:

public void open301(View view) {
  Intent openThree = new Intent(context,ThreeZeroOne.class);
  context.startActivity(openThree);
}

To start a new activity you will need a context to start from, and your current activity "BaseAdapter" is not a Context, luckly every view has a Context, so you can do like this:

public void open301(View view) {
    Intent openThree = new Intent(view.getContext(), ThreeZeroOne.class);
    view.getContext().startActivity(openThree);
}