Eurlar angles to Quaternion help

I want to use Quaternion because that way I can learn them but I am a bit lost on which one to use and how to use it. I have been looking at the reference pages but still a bit over my head.

Ok so what I want to do is to translate my current code into one that use Quaternion.

This is what I have, what it does is when the left or right trigger on a xbox pad is pressed it turns a guy and tilts him at the same time. I want to replace the tilt with the Quaternion because that way the player wont flip over and over on some rotational inputs.

 if(Input.GetAxisRaw("LT") > 0 )
     {
         transform.Rotate(-Vector3.up * Time.deltaTime * (Input.GetAxisRaw("LT")) * turnSpeed, Space.World);
         this.rigidbody.drag = .9;
         if(playerLRot < 25 || playerLRot > 340)
         {
             this.transform.Rotate(Vector3.forward * Time.deltaTime * 15);
             playerLRot = this.transform.eulerAngles.z;
         }
     }else if(Input.GetAxisRaw("RT") > 0 )
     {
         transform.Rotate(Vector3.up * Time.deltaTime * (Input.GetAxisRaw("RT")) * turnSpeed, Space.World);
         this.rigidbody.drag = .9;
         if(playerRRot > 340 || playerRRot < 25)
         {
             this.transform.Rotate(-Vector3.forward * Time.deltaTime * 15);
             playerRRot = this.transform.eulerAngles.z;
         }
         
     }
     
     //player is not turning
     if(!Input.GetAxisRaw("LT"))
     {
         if(playerLRot > 0)
         {
             this.transform.Rotate(-Vector3.forward * Time.deltaTime * 60);
             playerLRot = this.transform.eulerAngles.z;
         }
     }
     if(!Input.GetAxisRaw("RT"))
     {
         if(playerRRot >= 340 && playerRRot != 0)
         {
             this.transform.Rotate(Vector3.forward * Time.deltaTime * 60);
             playerRRot = this.transform.eulerAngles.z;
         }
     }

thanks for any help with this