1.    2D graphics (without the standard packages)

Since some inputs  in this notebook refer to the numbers of prior outputs before the evaluation do the following:
Kernel->Quit Kernel->Local->Quit

1.1. Plot

Plot[2  x^2 + 3  x - 2, {x, -3, 2}]

Options[Plot]

Plot[
      2  x^2 + 3  x - 2, {x, -3, 
        2}, 
AspectRatio -> Automatic]

Plot[
      2  x^2 + 3  x - 2, {x, -3, 
        2}, 
AspectRatio -> 
        Automatic, 
PlotRange -> {{-3, 
            2}, {-4, 3}}]

Plot[
      2  x^2 + 3  x - 2, {x, -3, 
        2}, 
AspectRatio -> 
        Automatic, 
PlotRange -> {{-3, 
            2}, {-4, 3}}, 
AxesLabel -> {x, y}, 
      Ticks -> None]

Plot[
      2  x^2 + 3  x - 2, {x, -3, 
        2}, 
AspectRatio -> 
        Automatic, 
PlotRange -> {{-3, 
            2}, {-4, 3}}, 
AxesLabel -> {x, y}, 
      Ticks -> 
        None, 
PlotStyle -> {AbsoluteThickness[2], 
          CMYKColor[0, 1, 1, 0], AbsoluteDashing[{2, 5}]}]

Plot[{2  x^2 + 3  x - 2, 2  x^2 + 3  x - 1, 2  x^2 + 3  x}, {x, -3, 
        2}, 
AspectRatio -> 
        Automatic, 
PlotRange -> {{-3, 
            2}, {-4, 3}}, 
AxesLabel -> {x, y}, 
      Ticks -> 
        None, 
PlotStyle -> {{AbsoluteThickness[2], 
            RGBColor[0, 1, 0]}, CMYKColor[0, 1, 1, 0], 
          AbsoluteDashing[{2, 5}]}]

1.2. Show

Plot[
      2  x^2 + 3  x - 2, {x, -3, 
        0}, 
PlotStyle -> {AbsoluteThickness[2], 
          RGBColor[0, 1, 0]}]

Plot[
      2  x^2 + 3  x - 1, {x, -1, 
        2}, 
PlotStyle -> {AbsoluteThickness[2], 
          RGBColor[1, 1, 0]}]

Plot[
      2  x^2 + 3  x, {x, -1.5, 
        0}, 
PlotStyle -> {AbsoluteThickness[2], 
          RGBColor[0, 0, 1]}]

Show[%, %%, %%%, 
AspectRatio -> 
        Automatic, 
PlotRange -> {{-3, 
            2}, {-4, 3}}, 
AxesLabel -> {x, y}, 
      Ticks -> None]

Plot[
      2  x^2 + 3  x - 2, {x, -3, 
        0}, 
PlotStyle -> {AbsoluteThickness[2], 
          RGBColor[0, 1, 0]}, 
DisplayFunction -> 
        Identity]

Plot[
      2  x^2 + 3  x - 1, {x, -1, 
        2}, 
PlotStyle -> {AbsoluteThickness[2], 
          RGBColor[1, 1, 0]}, 
DisplayFunction -> 
        Identity]

Plot[
      2  x^2 + 3  x, {x, -1.5, 
        0}, 
PlotStyle -> {AbsoluteThickness[2], 
          RGBColor[0, 0, 1]}, 
DisplayFunction -> 
        Identity]

Show[%, %%, %%%, 
AspectRatio -> 
        Automatic, 
PlotRange -> {{-3, 
            2}, {-4, 3}}, 
AxesLabel -> {x, y}, 
      Ticks -> 
        None, 
DisplayFunction -> $DisplayFunction]

Show[GraphicsArray[{%6, %7}]]

Show[GraphicsArray[{{%6, %7}, {%10, %11}}]]

1.3. Table

Table[i^2, {i, -5, 5, 1}]

g[a_][x_] := a*x^3

Table[g[a][x], {a, 1/4, 2, 1/4}]

Show[
      Table[Plot[g[a][x], {x, -2, 2}, 
          PlotRange -> {{-2, 2}, {-2, 
                2}}, 
                              AspectRatio -> 
            Automatic, 
                              DisplayFunction -> Identity],  {a, 1/4, 2, 
          1/4}], 
DisplayFunction -> $DisplayFunction]

\(Show[
      Table[Plot[\(g[a]\)[x], {x, \(-2\), 2}, 
          PlotRange -> {{\(-2\), 2}, {\(-2\), 
                2}}, 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ AspectRatio -> 
            Automatic, 
			PlotStyle -> {Hue[
                a/2]}, 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ DisplayFunction -> Identity], \ {a, 1/4, 2, 
          1/4}], 
DisplayFunction -> $DisplayFunction]\)

1.4. Animation by Table

h[a_][x_] := Sin[x + a]

Table[
Plot[h[a][x], {x, -Pi, 
          Pi}], 
{a, 0, 6, 6/21}]

\(Table[
Plot[\(h[a]\)[x], {x, \(-3\) Pi, 3  Pi}, 
        PlotRange -> {{\(-3\) Pi, 3  Pi}, {\(-1\), 
              1}}, 
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ AspectRatio -> Automatic, 
	
        PlotStyle -> {AbsoluteThickness[2], Hue[0.7], 
            AbsoluteDashing[{2, 4}]}, 
Axes -> None, 
        ImageSize -> {800, 100}], 
{a, 0, 6, 
        6/21}]\)

1.5.  ParametricPlot

ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 2  Pi}]

ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 
        2  Pi}, 
AspectRatio -> Automatic]

ellipse[a_, b_, p_, q_][t] := {a*Cos[t] + p, 
        b*Sin[t] + q}

ParametricPlot[ellipse[3, 2, -1, -1][t], {t, -Pi, 
        Pi}, 
AspectRatio -> Automatic]

ParametricPlot[
      Evaluate[ellipse[3, 2, -1, -1][t]], {t, -Pi, 
        Pi}, 
AspectRatio -> Automatic]

cycloid[a_, b_][t_] := {a*t - b*Sin[t], a - b*Cos[t]}

Table[cycloid[1, b][t], {b, 0.5, 1.5, 0.5}]

ParametricPlot[
      Evaluate[Table[cycloid[1, b][t], {b, 0.5, 1.5, 0.5}]], {t, 0, 
        4  Pi}, 
PlotStyle -> {Hue[0.7], Hue[1], 
          Hue[0.3]}, 
AspectRatio -> 
        Automatic]

1.6. Graphics Primitives

\(Show[
Graphics[{Hue[0.15], 
          Disk[{0, 0}, 2]}], 
Graphics[{Hue[0.7], 
          AbsoluteThickness[3], 
          Circle[{0, 0}, 2]}], 
Graphics[
        Polygon[{{0, 0}, {\(-1\), \(-2\)}, {\(-3\), 
              2}}]], 
Graphics[{Hue[1], 
          AbsoluteThickness[2], 
          Line[{{\(-1\), \(-2\)}, {\(-3\), 2}, {0, 
                0}, {\(-1\), \(-2\)}}]}], 
Graphics[{Hue[
            0.8], AbsoluteThickness[2], 
          Line[{{0, 0}, {5, 0}}]}], 
Graphics[{Hue[0.3], 
          AbsolutePointSize[10], 
          Point[{0, 0}]}], 
Graphics[{Hue[1], 
          AbsolutePointSize[5], 
          Point[{0, 0}]}], 
Graphics[{Hue[1], 
          Text[letters, {4.5, 0.2}]}], 
Graphics[{Hue[1], 
          Text[FontForm["letters", {"Arial", 
                16}], {4.5, \(-0.2\)}]}], 
AspectRatio -> Automatic]\)

1.7. ListPlot

ListPlot[{5, 5, 3, 6, 6, 7, 8, -1}]

ListPlot[{5, 5, 3, 6, 6, 7, 8, -1}, 
      PlotStyle -> {Hue[0.1], 
          AbsolutePointSize[8]}, 
AspectRatio -> 
        Automatic, 
      AxesOrigin -> {0, 0}, 
Frame -> 
        True]

ListPlot[{{-5, 5}, {-4, 2}, {0, 0}, {3, 1}, {5, 5}}, 
      PlotStyle -> {Hue[1], AbsolutePointSize[8]}]

ListPlot[{{-5, 5}, {-4, 2}, {0, 0}, {3, 1}, {5, 
          5}}, 
PlotJoined -> True, 
      PlotStyle -> {Hue[1], AbsoluteThickness[2]}]

ListPlot[Table[{x, x^2}, {x, -2, 2, 0.2}], 
      PlotStyle -> {Hue[1], AbsolutePointSize[8]}]

ListPlot[
      Table[{x, x^2}, {x, -2, 2, 
          0.2}], 
PlotJoined -> True, 
      PlotStyle -> {Hue[0.7], AbsoluteThickness[2]}]

k[x_] := (x + 1)^2 /; x <= 0
k[x_] := (x - 1)^2 /; x > 0

ListPlot[
      Table[{x, k[x]}, {x, -4, 4, 
          0.2}], 
PlotRange -> {{-4, 4}, {-4, 
            4}}, PlotStyle -> {Hue[0.3], 
          AbsolutePointSize[8]}]

1.8. Examples of animation

1.7.1. deltoid

deltoid[r_][t_] := 
      r*{2  Cos[t/3] + Cos[2  t/3], 2  Sin[t/3] - Sin[2  t/3]}

Table[
      Show[
Graphics[{CMYKColor[0.2, 0, 0.1, 0], 
            Disk[{0, 0}, 3]}], 
Graphics[
          Circle[{0, 0}, 
            3]], 
Graphics[{CMYKColor[0, 0.2, 0.4, 0], 
            Disk[{2  Cos[i/3], 2  Sin[i/3]}, 
              1]}], 
Graphics[
          Circle[{2  Cos[i/3], 2  Sin[i/3]}, 
            1]], 
Graphics[{AbsolutePointSize[5], 
            Point[{2  Cos[i/3], 
                2  Sin[i/
                      3]}]}], 
Graphics[{AbsolutePointSize[
              9], Hue[1], 
            Point[Evaluate[deltoid[1][
                  i]]]}], 
Graphics[{AbsoluteThickness[2], 
            Line[{{2  Cos[i/3], 2  Sin[i/3]}, 
                Evaluate[deltoid[1][
                    i]]}]}], 

ParametricPlot[
          Evaluate[deltoid[1][t]], {t, 0, 
            i}, 
PlotStyle -> {{Hue[0.7], 
                AbsoluteThickness[3]}}, 
          DisplayFunction -> 
            Identity], 

Axes -> 
          False, PlotRange -> {{-3.5, 3.5}, {-3.5, 
              3.5}}, 
AspectRatio -> 
          Automatic, 
DisplayFunction -> $DisplayFunction], 

{i, Pi/30, 6  Pi, 
        Pi/15}]

1.7.2. cycloid

cycloid[a_, b_][t_] := {a*t - b*Sin[t], a - b*Cos[t]}

circ = 
Graphics[{CMYKColor[0, 0.1, 0.3, 0], 
          Disk[{i, 1}, 1]}]

curve[a_, b_][i_] := 
ParametricPlot[
        Evaluate[cycloid[a, b][t]], {t, -Pi/100, i}, 
        PlotStyle -> {AbsoluteThickness[3], Hue[0.7]}, 
        DisplayFunction -> Identity]

cent = 
Graphics[{AbsolutePointSize[4], 
          Point[{i, 1}]}]

rad1 = 
Graphics[{AbsoluteThickness[2], 
          Line[{{i, 1}, Evaluate[cycloid[1, 1.5][i]]}]}]

rad2 = 
Graphics[{AbsoluteThickness[2], 
          Line[{{i, 1}, Evaluate[cycloid[1, 1][i]]}]}]

rad3 = 
Graphics[{AbsoluteThickness[2], 
          Line[{{i, 1}, Evaluate[cycloid[1,  .5][i]]}]}]

lin = 
Graphics[{AbsoluteThickness[1], 
          Line[{{-Pi/2, 0}, {13  Pi/2, 0}}]}]

circum = 
Graphics[{Circle[{i, 1}, 1]}]

po1 = 
Graphics[{AbsolutePointSize[6], Hue[1], 
          Point[Evaluate[cycloid[1, 1.5][i]]]}]

po2 = 
Graphics[{AbsolutePointSize[6], Hue[1], 
          Point[Evaluate[cycloid[1, 1][i]]]}]

po3 = 
Graphics[{AbsolutePointSize[6], Hue[1], 
          Point[Evaluate[cycloid[1,  .5][i]]]}]

Table[
Show[circ, curve[1, 1.5][i], cent, rad1, 
        lin, circum, 
        po1, 
AspectRatio -> 
          Automatic, 
PlotRange -> {{-Pi/2, 
              13  Pi/2}, {-1, 3}}, 
Axes -> False, 
        Background -> 
          Hue[0.7, 0.2, 
            0.9], 
DisplayFunction -> $DisplayFunction, ImageSize -> {800, 150}], 
{i, 0, 
        6  Pi, Pi/10}]

Table[
      Show[GraphicsArray[
{{Show[
                circ, curve[1, 1.5][i], cent, rad1, lin, circum, 
                po1, 
AspectRatio -> Automatic, 
                PlotRange -> {{-Pi/2, 13  Pi/2}, {-1, 
                      3}}, 
DisplayFunction -> 
                  Identity]}, 
{Show[
                circ, curve[1, 1][i], cent, rad2, lin, circum, 
                po2, 
AspectRatio -> Automatic, 
                PlotRange -> {{-Pi/2, 13  Pi/2}, {-1, 
                      3}}, 
DisplayFunction -> 
                  Identity]}, 
{Show[
                circ, curve[1,  .5][i], cent, rad3, lin, circum, 
                po3, 
AspectRatio -> Automatic, 
                PlotRange -> {{-Pi/2, 13  Pi/2}, {-1, 
                      3}}, 
DisplayFunction -> 
                  Identity]}}], 
Axes -> False, 
        Background -> Hue[0.7, 0.2, 0.9], 
        DisplayFunction -> $DisplayFunction, 
        ImageSize -> {800, 450}], 
{i, 0, 6  Pi, 
        Pi/10}]