Discourse markers: admittedly, that said

Admittedly, that said, by contrast, on the whole, mind you: words that guide the reader through a text.

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Discourse markers are words and phrases that show how a sentence connects to what came before, or what the speaker thinks about it. They don't change the facts; they guide the listener or reader. Most of them start a sentence and have a comma after them. Using the right one, and not too many, is a mark of C1 writing.

Job	Markers
accept a point, then contrast	admittedly, granted, that said, having said that, even so, all the same
compare or contrast	by contrast, in contrast, on the other hand, conversely, similarly, likewise
add a stronger point	what's more, besides, moreover, furthermore
result	as a result, consequently, therefore, thus
sum up	on the whole, all in all, by and large, in short, overall
comment	frankly, needless to say, understandably, surprisingly
in conversation	anyway, by the way, mind you, actually, as I was saying

Accepting a point, then disagreeing

Admittedly and granted accept that something is true. That said, having said that, even so and all the same then bring in the contrast.

Admittedly, the hotel was expensive. That said, the service was excellent.
Granted, he has a lot of experience, but he's not right for this job.
The film is far too long. Having said that, the acting is superb.
It was only a small mistake. Even so, she should have told us.
Incorrect: It was a small mistake. Even though, she should have told us.
Correct: It was a small mistake. Even so, she should have told us.
Even though joins two clauses; even so starts a new sentence.

Contrast and comparison

By contrast and in contrast compare two different things. On the contrary is different: it says that the opposite of the last statement is true.

My brother loves football. By contrast, I can't stand it.
Sales in Europe fell. On the other hand, sales in Asia rose by 10%.
"Was the film boring?" "On the contrary, it was gripping."
No, the opposite is true.
Incorrect: My brother loves sport. On the contrary, I hate it.
Correct: My brother loves sport. By contrast, I hate it.
On the contrary answers a statement and says it is wrong; it doesn't compare two people.
Prices went up in March. Similarly, wages rose slightly.

Adding and building an argument

Moreover and furthermore are formal. What's more is neutral to informal. Besides adds another reason, often a stronger one, in speech and informal writing.

The plan is too expensive. Moreover, it would take years to complete.
The flat is in the centre, and what's more, it's cheap.
I don't want to go out tonight. Besides, I've got nothing to wear.

Result and summing up

The road was closed. As a result, we were two hours late.
Demand fell sharply; consequently, the factory closed.
There were a few problems, but on the whole the trip was a success.
By and large, the public supported the plan.
All in all, it was a good year for the company.

Comment and attitude

Some markers show the writer's view of what follows.

Frankly, I don't think it will work.
Needless to say, the trip was cancelled.
As you would expect.
Understandably, the residents were angry.
Surprisingly, nobody noticed.

In conversation: anyway, mind you, actually

Anyway, let's get back to the main point.
Returning to the topic, or ending it.
By the way, did you call your mum?
Changing the topic.
The food was awful. Mind you, it was cheap.
A small point on the other side; typical of British English.
"Is it your first time here?" "Actually, I've been twice before."
In fact, contrary to what you think.

Actual and actually are false friends for Russian speakers. Actually means "in fact", often correcting what someone thinks; it does not mean "now". Eventually means "in the end, after a long time".

I thought she was Spanish, but actually she's Italian.
At the moment, I'm working on a new project.
For "now", use at the moment or currently.
We waited for hours, but eventually the bus came.
Incorrect: Climate change is a very actual topic.
Correct: Climate change is a very topical subject.
The adjective actual means "real", not "current".