A comma is a short pause within a sentence, added to help the reader understand your meaning. A number of examples from the PhraseBook are given below:

Their study, like that of X, is influenced by …
The results suggest, contrary to current theory, that …
X claims, in my view wrongly, that …
This does not mean, however, that …

Interestingly, some studies show …
However, recent research suggests that …

To investigate whether …, we examined …
Similar results have been found in …, suggesting that …
If this is the case, then …

Commas in series

In US English, a comma is normally added in a series of three or more items, as in the examples below:

New York, Washington, and San Francisco
New York, Washington, or San Francisco

But not in British English:

England, Scotland and Wales
England, Scotland or Wales

However, always add a comma, both in British and US English, if the penultimate item includes and or or:

Einstein, Watson and Crick, and Rutherford have all been awarded Nobel Prizes.

And in cases of ambiguity, use a comma to make a clear distinction between items:

Patients’ responses were recorded as none, mild, moderate or severe.
Patients’ responses were recorded as none, mild, moderate, or severe.

The wide-ranging discussion covered not only human rights, but also corruption and the United Nations.
The wide-ranging discussion covered not only human rights, but also corruption, and the United Nations.

Comma with i.e., e.g. and etc.

In US English, a comma is normally added after i.e. and e.g. and before etc., for example:

Smith’s paper, i.e., her most recent work, is widely cited.
Smith’s work, e.g., her most recent paper, is widely cited.
Smith’s papers, books, findings, etc. are widely cited.

But in British English i.e., e.g. and etc. are written without a comma:

Smith’s paper, i.e. her most recent work, is widely cited.
Smith’s work, e.g. her most recent paper, is widely cited.
Smith’s papers, books, findings etc. are widely cited.

Comma with respectively

In US English, a comma is normally used with respectively, for example:

The results were 40% and 50% for men and women, respectively.

But in British English, respectively is usually written without a comma:

The results were 40% and 50% for men and women respectively.