Btukfyl

There are some ways to put the figures side by side such as subfig (which is not recommended), subfigure, subcaption, subcaptionbox and minipage. I tried minipage and subcaption and here the codes and results:

minipage:

documentclass{article} %Document type

usepackage{amssymb,amsmath} %Inserting symbols

usepackage{graphicx} %Inserting graphics

usepackage{fullpage} 

usepackage{indentfirst} %Indentation of the first paragraphs

usepackage{float} %Forcing exact graphic placement - H

usepackage{chngcntr} %Required package in order to use the macro.

counterwithin{figure}{section} %Macro: Article class - per-section numbering for figure

counterwithin{equation}{section} %Macro: Article class - per-section numbering for equation

counterwithin{table}{section} %Macro: Article class - per-section numbering for tables

usepackage{physics} %In order to type PDEs easily

usepackage{bm} %Bold math symbols

usepackage{booktabs} %Making tables

usepackage{subcaption} %subfigure and subtable environment

begin{document}

This is a test document in order to put figures side by side, increase/decrease the sizes of the figures and align horizontally.    

begin{figure}[H]

centering

begin{minipage}{.45linewidth}

    includegraphics[width=linewidth]{./Figures/actual.png}

    caption{First caption}

    label{img1}

end{minipage}

hspace{.05linewidth}

begin{minipage}{.45linewidth}

    includegraphics[width=linewidth]{./Figures/master.png}

    caption{Second caption}

    label{img2}

end{minipage}

end{figure}

end{document}

subcaptionbox:

begin{figure}[H]

centering

subcaptionbox{Actual Elementlabel{actual-element}}

{%

    includegraphics[width=0.48columnwidth]{./Figures/actual.png}

    hspace{0.04columnwidth}

}%

subcaptionbox{Master Elementlabel{master-element}}

{%

    includegraphics[width=0.48columnwidth]{./Figures/master.png}

    hspace*{fill}

}%

caption{Coordinate Transformation}label{animals}

end{figure}

The result is

As it is seen, both of the results are the same.

I want to make this two figures closer and bigger. These figures should not exceed the linewidth and should center the page.

The problem is mostly due to the .png images having extra wide space around them. Please check your images or try to upload them in your post. Here is your code with experimental images:

documentclass{article} %Document type

usepackage{amssymb,amsmath} %Inserting symbols

usepackage{graphicx} %Inserting graphics

usepackage{fullpage} 

usepackage{indentfirst} %Indentation of the first paragraphs

usepackage{float} %Forcing exact graphic placement - H

usepackage{chngcntr} %Required package in order to use the macro.

counterwithin{figure}{section} %Macro: Article class - per-section numbering for figure

counterwithin{equation}{section} %Macro: Article class - per-section numbering for equation

counterwithin{table}{section} %Macro: Article class - per-section numbering for tables

usepackage{physics} %In order to type PDEs easily

usepackage{bm} %Bold math symbols

usepackage{booktabs} %Making tables

usepackage{subcaption} %subfigure and subtable environment

begin{document}

This is a test document in order to put figures side by side, increase/decrease the sizes of the figures and align horizontally.    

begin{figure}[H]

centering

begin{minipage}{.48linewidth}

    includegraphics[width=linewidth]{example-image-A}

    caption{First caption}

    label{img1}

end{minipage}

hfill

begin{minipage}{.48linewidth}

    includegraphics[width=linewidth]{example-image-B}

    caption{Second caption}

    label{img2}

end{minipage}

end{figure}

end{document}

And here is a low-quality version of your .png images copied from your post:

As you see, the images now have thinner space in-between and are larger. I've cut any extra white space around each one on my computer.

I have one question. If I have to give one main caption below these figures. How can i make a change in the above mentioned code?