Hello, i'm Timon and i'm glad to help you.
The email seems legit, but, generally speaking, you should avoid clicking on link in email.
If possible, use bookmarks or type manually the URL you want to reach.
Indeed, you can check your Microsoft's account activity here: https://account.microsoft.com/security/
Here you will find some useful information, such as the date your account was accessed, by which device, with which IP address.
If you find something wrong, i strongly advise you to change your password and recommend to use the two-step verification.
https://support.microsoft.com/en-us/help/12408/...
https://support.microsoft.com/en-us/help/10494/...