The concepts are simpler and i have explained below. Remainin is mathemaatics and equations, that you have to workout a lot of examples without which you cant fully learn and perform for exams.
1. fourier transform -Any signall of whatever the shape can be experrssed as a summation of some frequency components. If the summatioin contains A continous frequency distribution (THat means it has all ferquencies from 0 to innfinity) then it is called fourier transform. (If simply fourier transform is mentioned, it means 'continuous' that means it has a spectrum from 0 to infinity)
2. Fourier series- The same conncept as above but for periodic functions.
3.Discrete time fourier transform-DTFT-Thi is equivalent to fourier transform as explained in 1. But this is a a sampled content of fourier trasnsform. For computers, it has to be sampled all data isn't it? That is why instead of fourier transform, DTFT is being used in computers ffor analysis.
4. Discrete fourier transform- DFT-THis is equivalent to as explained in 2, but a sampled content of what were in fourier series. Simply , for periodiic funcitons, it can be expressed as sum of some frequency components equally spaced.
It is better you to create a table like this
Continuos ffrequency sampled frequency
Non periodic signals FT | DTFT
-------- |--------------
Periodic signals FS | DFT