I am trying to understand how transactions, credit cards (magstripes, chips, ..), e-commerce,.. work from a cryptographic perspective. What kind of algorithms are used, how to ensure Confidentiality, Integrity, authentication, ... Thank you in advance
That's a mighty big subject, much too large to adequately handle here.
However, Bruce Schneier is one of the world's foremost authorities on security and he has over the years written quite a number of very approachable books. Here's a link to a list of all his current books:
https://www.goodreads.com/author/list/175417.Bruce_Schneier
In addition, the payment processing industries have a requirement called "PCI Compliance" which all participants must comply with. Their web-site has materials that are introductory, as well:
https://www.pcicomplianceguide.org/
Hope this helps!
As you're approaching your understanding of this subject, bear in mind that the requirement is not simply that "the data in transit must not be understood," but that the parties must know (a) who it is that they are talking to, and (b) that each message is received "exactly as tendered," and with no messages inserted nor left out. And, the total requirement quickly goes well beyond cryptography, to the underlying protocols that are employed across these cryptographically-secure connections. Quite a big subject.