How to make a centered, non-bold abstract and section titles

Question

I'm writing a paper on Overleaf, but I have a couple of issues. Firstly, when I use begin{abstract}...\end{abstract} the word 'Abstract' comes up in bold and centered above the text, with only the A in capitals, as shown below.

How can I

1. Make the word Abstract all in capitals
2. Make the word Abstract not in bold
3. Make the word Abstract next to the text, eg like in this paper

Please note; I don't necessarily want to change all these things all at once, I'd like to be able to change them one at a time preferably.

Secondly, I'd like to make similar chapters and sections titles eg to the ones in the aforementioned paper. I am currently using \begin{section]...\end{section} but the section titles come out in bold and are on the left of the page; I'd like each new section title to be like the ones in the aforementioned article; ie centered and not in bold (as well as in capitals hopefully), while still above the text.

Thank you for your help.

This is my preamble: \documentclass[12pt, letterpaper]{article} \usepackage[utf8]{inputenc} \usepackage{amssymb,amsmath,amsthm}

Answer 1

Here is how to obtain what you want for section titles. I used the titlecaps package to have the first letter of each (significant) word capitalised, which looks better with small caps, in my opinion, and the § symbol before the section number. Of course, you just have to remove it from the code if you don't like it.

 \documentclass[12pt, letterpaper]{article}
 \usepackage{erewhon}
 \usepackage{amssymb,amsmath,amsthm}
 \usepackage[runin]{abstract}
 \usepackage{titlesec}
 \usepackage{titlecaps}
\usepackage{lipsum}
\renewcommand{\abstractname}{\normalfont\scshape{Abstract}.}

 \begin{document}

 \title{A Paper} \author{Me } \date{Today} \maketitle
 \titleformat{\section}[block]{\filcenter\scshape}{\S\,\thesection.}{0.5em}{\titlecap}
 \section{First Section}
 \lipsum[11]

\end{document} 

Answer 2

Hope this may helps you:

\documentclass[12pt, letterpaper]{article}
\usepackage[utf8]{inputenc} 
\usepackage{amssymb,amsmath,amsthm} 
\usepackage[runin]{abstract}
\begin{document}

\renewcommand{\abstractname}{\normalfont\scshape{Abstract}.}

\title{Title}

\author{Author}

\maketitle

\begin{abstract}
This is for test
\end{abstract}

\end{document}

Output