You have loaded the package ragged2e with the document option, that kills indents and typesets the document in raggedright fashion, which I don't think is what you want.
I've also made some changes to your input, so that it's more easily manageable. Note that commands such as \Large don't take an argument, but set their action to continue until countermanded by another command or the end of the group where they have been issued.
Note also that a paragraph is ended by simply leaving an empty line in the source code.
\documentclass[12pt,a4paper]{article}
%% Packages
\usepackage{amsmath} % must go before fontspec
\usepackage{fontspec}
\usepackage{polyglossia}
\usepackage[
top=2.5cm,
left=3cm,
bottom=2.5cm,
right=2.5cm
]{geometry}
\usepackage{graphicx}
\usepackage{units}
\usepackage{pstricks}
\usepackage{float}
\usepackage{wrapfig}
\usepackage{setspace}
\usepackage{ragged2e}
\usepackage[nottoc]{tocbibind}
\usepackage{titlesec}
\usepackage{indentfirst}
\usepackage{pgfplots}
\usepgfplotslibrary{polar}
\usepgflibrary{shapes.geometric}
\usetikzlibrary{calc}
\pgfplotsset{compat=1.8}
\pgfplotsset{
pa/.append style={
axis x line=bottom,
axis y line=left,
xlabel={$r; \cdot 10^7 m$},
ylabel={$F_{pa}; \cdot 10^8 N$}
}
}
%% Fonts and languages
\setmainfont[Ligatures=TeX,
SmallCapsFont=TeX Gyre Termes,
SmallCapsFeatures={Letters=SmallCaps}
]{Times New Roman}
\setdefaultlanguage{latvian}
\setotherlanguages{english, russian}
%% Misc settings
\titleformat{\section}[block]
{\color{black}\Large\bfseries\filcenter}
{}
{1em}
{}
\makeatletter
\renewcommand\@biblabel[1]{#1.}
\makeatother
\numberwithin{equation}{subsection}
\numberwithin{figure}{subsection}
\numberwithin{table}{subsection}
\onehalfspacing
\setlength\parindent{24pt}
\begin{document}
\begin{titlepage}
\centering
{\large\scshape
University \\
Department \\
Faculty
\par}
\vspace*{\fill}
{\Large
name
\par}
{\Large\bfseries
Topic
\par}
{\Large
Study
\par}
\vspace*{\fill}
\raggedleft
{\large
Work advisor: \\
Professor
\par}
\vspace{\fill}
\centering
{\large\scshape
City, Year
\par}
\end{titlepage}
\tableofcontents
\clearpage
\section*{Abstrakts}
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Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.
\end{document}
I give it a try:
Standard Behaviour
The standard paragraph shows an indentation in the first line and no space between paragraphs (\parskip is zero).
\documentclass{article}
\usepackage{blindtext}
\begin{document}
\blindtext
\blindtext
\end{document}
Standard Document Class Solution
You can use the parskip package (CTAN link) to solve your problem.
From the documentation:
Package to be used with any document class at any size. It produces
the following Paragraph Layout:
Zero Parindent and non-zero Parskip.
The stretchable glue in \parskip helps LaTeX in finding the best place
for page breaks.
In addition, the package adjusts the skips between
list items.
This package is no more than quick fix; the ‘proper’ way to achieve
effects as far-reaching as this is to create a new class. An example
class is to be found in the ntgclass set: artikel3.cls
The koma-script bundle classes and the memoir class all provide
similar functionality, and their respective documentation files
discuss the pros (such as they are) and cons of this approach.
\documentclass{article}
% new package
\usepackage{parskip}
\usepackage{blindtext}
\begin{document}
\blindtext
\blindtext
\blindlist{itemize}
\end{document}
Bad Solution: Manually Change the Lengths
Important for you is that the package parskip takes care of other things too. Sometimes you see people manually changing the parameters like \setlength{\parindent}{0em} and \setlength{\parskip}{1em} but this is considered bad because it also could change the distance between items in lists and so on. But I am not an expert here.
Alternative Solution: KOMA Approach
There are the so called KOMA-Script (CTAN link) document classes (in contrast to the standard document classes like article and book).
They offer a document class option called parskip which also "takes care of everything".
\documentclass[parskip]{scrartcl}
\usepackage{blindtext}
\begin{document}
\blindtext
\blindtext
\blindlist{itemize}
\end{document}
PS: I don't get the
\section*{\hspace{150pt} Motivation}
\hspace{10pt}\begin{normalsize}
part of your code.
Best Answer
Set the
\parindentlength to the desired value:A complete example using your code: