Unable to display File Contents of my Hard Drive

Hello everyone!
I bought a SATA 2.5 external enclosure in which I put my internal hard drive into an external hard drive. The problem is that when I plug the external hard drive on another PC that it recognizes the three partitions of my hard drive (C, D, F) but does not display file contents. When I try to enter the scores he asks me to format the drive. Also, when I go into the drive properties it shows that all space is used.
What should I do? Do I have to format it? But I fear losing all my data. Help me please!
