Usually we indicate a start of a new paragraph by indenting the first line. Are there any alternative ways of doing so?
I prefer to use space between paragraphs and no indent at all. Usually, a 1,5mm to 2,5mm does the job, according to your leading/layout.
There is also negative indent: the first like begins at the marign and the remaining are indented. To get this you apply a left indent to the paragraph (say, 10mm) and a negative indent to the first one (-10mm).
Except this, I don't see other good ways. In onder times there are bullets marking the begin of a paragraph (as you may find in some iluminuras and medieval documents). But this is hardly a choice for any contemporary text.
Ken, indenting the first line is the traditional way to do this, but not the only one. The reason to use an indent is to indicate "this is a new paragraph". But if you have another graphic resource to do this –as space between paragraphs– it's perfectly valid if it fits your layout.
Space between paragraphs was a difficult thing to use until electronic desktop publishing arrived. Text pages were set based on leading grid and everything needed to fit in a multiple of the leading –say, 12pt, 24pt, 36pt etc. When there was another graphic element to clearly indicate a new paragraph (as a previous subtitle), the indent was not necessary.
Nowadays, you don't need to be limited to these grids. You can use measures like a 10.25pt type size in a 13.7pt leading without technical problem. You can also use space before and after paragraphs and then vertically justify the text to always fill the page limits.
Of course, most of the books still use the traditional way –indents and no space between paragraphs. It's more easy to do, always work and saves space. But this is a choice, not a rule.
You can see some great publications using the no-indent-with-space method, as London's New Left Review award-winning graphic project. It's especially good in layouts with generous margins. The negative indent is good to reference texts, as dictionaries, encyclopedias and technical glossaries. The way Nick described is also very interesting.
It really depends on the kind of publication.
In a book, where the verso shines through, you want to stick to your baseline grid, period.* Using arbitrary spaces between paragraphs may seem like a good idea in theory, and look good in InDesign too, but not once you hold the physical object in your hand and the stuff that shines through is shifted all over the place.
And I wouldn't even call that a limitation. It's being mindful of how the medium behaves, physically.
(* Unless of course you break it consciously, there's a reason for it, and you know what you're doing.)
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