Making paragraphs
To start a paragraph, just type some text. To end the current paragraph, put an empty line. This is three paragraphs, the separation of which is made by two empty lines.

It is a truth universally acknowledged, that a single man in possession
of a good fortune, must be in want of a wife.

However little known the feelings or views of such a man may be on his
first entering a neighbourhood, this truth is so well fixed in the minds
of the surrounding families, that he is considered the rightful property
of some one or other of their daughters.

``My dear Mr. Bennet,'' said his lady to him one day,
``have you heard that Netherfield Park is let at last?''

A paragraph separator is made of a sequence of at least one blank line, at least one of which is not terminated by a comment. A blank line is a line that is empty or made only of blank characters such as space or tab. Comments in source code are started with a % and span up to the end of line. In the following example the two columns are identical:

\documentclass[twocolumn]{article}
\begin{document}
First paragraph.

Second paragraph.
\newpage
First paragraph.
      
  % separator lines may contain blank characters.
  		
Second paragraph.
\end{document}

Once LaTeX has gathered all of a paragraph’s contents it divides that content into lines in a way that is optimized over the entire paragraph (see Line breaking).
There are places where a new paragraph is not permitted. Don’t put a blank line in math mode (see Modes); here the blank line before the \end{equation}

\begin{equation}
  2^{|S|} > |S|

\end{equation}

will get you the error ‘Missing $ inserted’. Similarly, the blank line in this \section argument

\section{aaa

bbb}

gets ‘Runaway argument? {aaa ! Paragraph ended before \@sect was complete’.

\par
Synopsis (note that while reading the input TeX converts any sequence of one or more blank lines to a \par, Making paragraphs):

\par

End the current paragraph. The usual way to separate paragraphs is with a blank line but the \par command is entirely equivalent. This command is robust (see \protect).
This example uses \par rather than a blank line simply for readability.

\newcommand{\syllabusLegalese}{%
  \whatCheatingIs\par\whatHappensWhenICatchYou}

In LR mode the \par command does nothing and is ignored. In paragraph mode, the \par command terminates paragraph mode, switching LaTeX to vertical mode (see Modes).
You cannot use the \par command in a math mode. You also cannot use it in the argument of many commands, such as the sectioning commands, e.g. \section (see Making paragraphs and \newcommand & \renewcommand).
The \par command is not the same as the \paragraph command. The latter is, like \section or \subsection, a sectioning command used by the LaTeX document standard classes (see \subsubsection & \paragraph & \subparagraph).
The \par command is not the same as \newline or the line break double backslash, \\. The difference is that \par ends the paragraph, not just the line, and also triggers the addition of the between-paragraph vertical space \parskip (see \parindent & \parskip).
The output from this example

xyz

\setlength{\parindent}{3in}
\setlength{\parskip}{5in}
\noindent test\indent test1\par test2

is: after ‘xyz’ there is a vertical skip of 5 inches and then ‘test’ appears, aligned with the left margin. On the same line, there is an empty horizontal space of 3 inches and then ‘test1’ appears. Finally. there is a vertical space of 5 inches, followed by a fresh paragraph with a paragraph indent of 3 inches, and then LaTeX puts the text ‘test2’.

\indent & \noindent
Synopsis:

\indent

or

\noindent

Go into horizontal mode (see Modes). The \indent command first outputs an empty box whose width is \parindent. These commands are robust (see \protect).
Ordinarily you create a new paragraph by putting in a blank line. See \par, for the difference between this command and \par. To start a paragraph without an indent, or to continue an interrupted paragraph, use \noindent.
In the middle of a paragraph the \noindent command has no effect, because LaTeX is already in horizontal mode there. The \indent command’s only effect is to output a space.
This example starts a fresh paragraph.

... end of the prior paragraph.

\noindent This paragraph is not indented.

and this continues an interrupted paragraph.

The data 

\begin{center}
  \begin{tabular}{rl} ... \end{tabular}
\end{center}

\noindent shows this clearly.

To omit indentation in the entire document put \setlength{\parindent}{0pt} in the preamble. If you do that, you may want to also set the length of spaces between paragraphs, \parskip (see \parindent & \parskip).
Default LaTeX styles have the first paragraph after a section that is not indented, as is traditional typesetting in English. To change that, look on CTAN for the package indentfirst.

\parindent & \parskip
Synopsis:

\setlength{\parindent}{horizontal len}
\setlength{\parskip}{vertical len}

Both are rubber lengths (see Lengths). They affect the indentation of ordinary paragraphs, not paragraphs inside minipages (see minipage), and the vertical space between paragraphs, respectively.
For example, if this is put in the preamble:

\setlength{\parindent}{0em}
\setlength{\parskip}{1ex}

The document will have paragraphs that are not indented, but instead are vertically separated by about the height of a lowercase ‘x’.
In LaTeX standard class documents, the default value for \parindent in one-column documents is 15pt when the default text size is 10pt, 17pt for 11pt, and 1.5em for 12pt. In two-column documents it is 1em. (These values are set before LaTeX calls \normalfont so em is derived from the default font, Computer Modern. If you use a different font then to set \parindent to 1em matching that font, put \AtBeginDocument{\setlength{\parindent}{1em}} in the preamble.)
The default value for \parskip in LaTeX’s standard document classes is 0pt plus1pt.

Marginal notes
Synopsis, one of:

\marginpar{right}
\marginpar[left]{right}

Create a note in the margin. The first line of the note will have the same baseline as the line in the text where the \marginpar occurs.
The margin that LaTeX uses for the note depends on the current layout (see Document class options) and also on \reversemarginpar (see below). If you are using one-sided layout (document option oneside) then it goes in the right margin. If you are using two-sided layout (document option twoside) then it goes in the outside margin. If you are in two-column layout (document option twocolumn) then it goes in the nearest margin.
If you declare \reversemarginpar then LaTeX will place subsequent marginal notes in the opposite margin to that given in the prior paragraph. Revert that to the default position with \normalmarginpar.
When you specify the optional argument left then it is used for a note in the left margin, while the mandatory argument right is used for a note in the right margin.
Normally, a note’s first word will not be hyphenated. You can enable hyphenation there by beginning left or right with \hspace{0pt}.
These parameters affect the formatting of the note:
\marginparpush 	Minimum vertical space between notes; default ‘7pt’ for ‘12pt’ documents, ‘5pt’ else. See also page layout parameters marginparpush.
\marginparsep 	Horizontal space between the main text and the note; default ‘11pt’ for ‘10pt’ documents, ‘10pt’ else.
\marginparwidth 	Width of the note itself; default for a one-sided ‘10pt’ document is ‘90pt’, ‘83pt’ for ‘11pt’, and ‘68pt’ for ‘12pt’; ‘17pt’ more in each case for a two-sided document. In two column mode, the default is ‘48pt’.
The standard LaTeX routine for marginal notes does not prevent notes from falling off the bottom of the page.