how to rotate camera on x and y axis with mouse?

Hello, I am a begginer on Unity, and right now I am working on a script for camera control. I found a script which allow my camera to follow the player and to rotate it with the mouse. That is great, but the problem is that this script allows to rotate the camera only on Y axis, and I want to rotate on X too. I know that there is a lot of other scripts which can do this thing, but this script is very simple for me and I wish to work on it. Please help me. This is the part of code for rotation :

if (RotateAroundPlayer)
Quaternion camTurnAngle =
Quaternion.AngleAxis(Input.GetAxis(“Mouse X”) * RotationsSpeed, Vector3.up);

        _cameraOffset = camTurnAngle * _cameraOffset;

Hi, would like to help but a few more info would be necessary to understand how the whole thing works.
Is _cameraOffset a Vector3, and how do you use it to rotate the cam (with transform.Rotate() ?)
Is RotateAroundPlayer a bool ?
Is the script attached to your cam ?