Creating a coordinate system with TikZ

Question

I would like to create a coordinate system as in the following picture, or at least similar.

I would really appreciate guidance.

Answer 1

Actually, this is quite easy if you follow TikZ manual. Here is my attempt:

\documentclass{standalone}
\usepackage{amssymb,amscd,amsmath}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
  \draw [thick, ->] (0,0) -- (0,7);
  \draw [thick, ->] (0,0) -- (7,0);
  \draw [fill] (0.1, 5) circle [radius=.5pt];
  \draw [fill] (6, 0.1) circle [radius=.5pt];
  \draw [->] (0.1,5) -- (6,0.1);
  \node [above] at (0,7) {$H^{\ast }$ (fiber)};
  \node [right] at (7,0) {$H^{\ast }$ (base)};
  \node [left]  at (0,5) {5};
  \node [below] at (6,0) {6};
  \node [above right] at (0.1,5) {$\pi _{4}S^{3}$};
  \node [above right] at (6,0.1) {$\mathbb{Z}_{2}\cdot l_{3}^{2}$};
\end{tikzpicture}

\end{document}

By the way, I'm not quite sure the meaning of your lines in pencil, therefore I did not draw it in my example. However, you should learn from the code above.