When it comes to supporting Docker then almost all CI/CD options support Docker It is impossible for one to compete without having docker support.
There are two kinds of CI/CD options available:-
Saas Products: Saas builds generally happen somewhere outside your infrastructure. They do have inhouse options which generally come with enterprise license hence way too costly. Like TravisCI and CircleCI, some of the alternatives are:
Bamboo From Atlassian hence has nicer integration with the rest of the Atlassian’s products.
Open-source Tools: Open-source tools generally run in the house. Some of the popular ones are:
Jenkins is now, developed/maintained by Cloudbees folks: Project build configuration exists as Jenkins configuration (personally I prefer that being part of the project configuration).
If you want to learn Docker then I would suggest you must take up the following docker training course. I am also mentioning a video tutorial which I would suggest you must watch to learn all the basics of Docker.