Here are some answers to your questions.
The "space" you are referring to is the paragraph indent, and it is automatically added to each new paragraph (which in your LaTeX source is created by adding a blank line between pragraphs.) It may also be added automatically at the end of certain environments.
The default for most document classes is to indent every new paragraph except for those immediately following a chapter/section/subsection heading.
- To remove the indent in a single paragraph, use the
\noindent
command. You shouldn't generally need to do this, however. If you find indented paragraphs after an environment (e.g. displayed math) that you don't need, you should make sure there is no blank line in your source after the environment. It's helpful to insert a %
on a line by itself in these cases to make your source more readable.
- When to break a paragraph and when not to is a writing question: it has no direct objective answer, although roughly a paragraph corresponds to a single idea. Here is a link to a reasonable explanation: Paragraphs and paragraphing.
- If you are indenting new paragraphs, there is no need to insert blank lines in the output between paragraphs. (Of course your source document will use blank lines to separate paragraphs.)
- In general, you shouldn't use
\\
to create blank lines. The \\
command inserts a line break within a single paragraph. As Werner says in his answer, line spacing around headings should be done by the heading definition, and not manually. If you do need to make a blank line, on an exceptional basis, you can insert space with the \bigskip
commands (or \vspace{})
command, or but generally you shouldn't have to do this. See What is an elegant way to insert a skip between two paragraphs?.
For some documents (not regular reports/articles/theses/books) it is sometimes appropriate to have no paragraph indentation, and separate paragraphs with blank lines. If you need this kind of format, you should use the parskip
package.
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