I am about to take an undergraduate course in Mathematical logic any textbooks to recommend.Want it to be rigorous and not missing things. I am an Math undergraduate. Got still 2 years for my degree. I have taken courses mostly in Algebra (ring theory etc.). Also taken Real analysis courses. So my mathematical maturity is mediocre I would say. (I have also done calculus courses etc on my first year.)
Take a look at my Teach Yourself Logic Study Guide, which gives a lot of detailed advice about logic books at different levels, suitable to different backgrounds.
Check out the proposed syllabus of the course you are about to start to see what it covers and hence what's relevant in the Guide.
I would recommend Cori and Lascar's Mathematical Logic: A Course with Exercises. It has a lot of examples from algebra, so is appropriate for a math major who has taken abstract algebra.