Transitions help your writing flow.  Your choice of transition signals to the reader what connections you are making between paragraphs or sentences. I am categorising them by the type of connection or relationship they suggest.

Acknowledgement of counter claims

acknowledging, although, aside from, despite, even though, granted that, of course, it is true that, others may claim, 

Addition - suggesting a similar idea

again, also, another, as a result, as well as, besides, both x and y, consequently, equally important, finally, first, for example, for instance, further, furthermore, in addition, in fact, in the same way, likewise, moreover, next, not only a but also b, similarly, therefore, thus, too,

Contrast and Comparison - suggesting a difference

at the same time, but, but rather, conversely, however, in contrast, in spite of, instead, nevertheless, nor, on one hand, on the contrary, on the other hand, still, while this may be true, yet

Illustration - giving evidence

a few examples are, as an example, as an illustration, for example, for instance, for one thing, illustrated by, including, in particular, in this case, namely, specifically, such as, this is especially true when, to illustrate, x highlights this