How can i rotate the camera with the mouse around the player?

Question

Now it's rotating in space i can rotate the camera around but not around the player. I want the camera to be rotating only around the player.

using UnityEngine;
using System.Collections;

public class CameraMover : MonoBehaviour
{
    public float speedH = 2.0f;
    public float speedV = 2.0f;
    private float yaw = 0.0f;
    private float pitch = 0.0f;

    public Transform playerTransform;
    public Transform mainCameraTransform = null;
    private Vector3 cameraOffset = Vector3.zero;
    public float turnSpeed = 3;

    void Start()
    {
        mainCameraTransform = Camera.main.transform;

        //Get camera-player Transform Offset that will be used to move the camera 
        cameraOffset = mainCameraTransform.position - playerTransform.position;
    }

    void LateUpdate()
    {
        //Move the camera to the position of the playerTransform with the offset that was saved in the begining
        mainCameraTransform.position = playerTransform.position + cameraOffset;

        yaw += speedH * Input.GetAxis("Mouse X");
        pitch -= speedV * Input.GetAxis("Mouse Y");
        mainCameraTransform.eulerAngles = new Vector3(pitch, yaw, 0.0f);
    }
}

I'm using now eulerAngles for the rotation.

Answer 1

As mentioned in the comments you need to create a parent object for the camera, and rotate that object instead of the camera. Try this code:

using UnityEngine;
using System.Collections;

public class CameraMover : MonoBehaviour
{
    public float speedH = 2.0f;
    public float speedV = 2.0f;
    private float yaw = 0.0f;
    private float pitch = 0.0f;

    public Transform playerTransform;
    public Transform mainCameraTransform = null;
    private Vector3 cameraOffset = Vector3.zero;
    public float turnSpeed = 3;

    // Create a camera parent object
    GameObject cameraParent;

    void Start()
    {
        cameraParent = new GameObject();
        mainCameraTransform = Camera.main.transform;

        //Get camera-player Transform Offset that will be used to move the camera 
        cameraOffset = mainCameraTransform.position - playerTransform.position;

        // Position the camera parent to the player and add the camera as a child
        cameraParent.transform.position = playerTransform.position;
        mainCameraTransform.parent = cameraParent.transform;
    }

    void LateUpdate()
    {
        //Move the camera to the position of the playerTransform with the offset that was saved in the begining
        //mainCameraTransform.position = playerTransform.position + cameraOffset;

        yaw += speedH * Input.GetAxis("Mouse X");
        pitch -= speedV * Input.GetAxis("Mouse Y");

        // Rotate the camera parent instead of the camera
        cameraParent.transform.eulerAngles = new Vector3(pitch, yaw, 0.0f);
    }
}