f[x_, y_] := 2 - x^2 - y^2
Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}]

f[x_, y_] := Sqrt[x^2 + y^2]
Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}]

f[x_, y_] := Sqrt[x^2 + y^2]
Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}, 
      ViewPoint -> {-1.337,  -2.473,  0.693}, 
      BoxRatios -> {4, 4, 3}]

f[x_, y_] := Max[Abs[x], Abs[y]]
Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}, PlotPoints -> 50, 
      ViewPoint -> {-1.337,  -2.473,  0.693}]

Remove[ImplicitPlot]

Needs["Graphics`ImplicitPlot`"]

f[x_, y_] := Sqrt[x^2 + y^2]
Plot3D[
      f[x, y], {x, -2, 2}, {y, -2, 2}]
ImplicitPlot[
      f[x, y] == 1, {x, -2, 2}, {y, -2, 
        2}]
ImplicitPlot[
      Table[f[x, y] == c, {c, 0.1, 2, 0.1}], {x, -2, 
        2}, {y, -2, 2}, PlotPoints -> 50]

f[x_, y_] := Max[Abs[x], Abs[y]]
Plot3D[
      f[x, y], {x, -2, 2}, {y, -2, 2}]
ImplicitPlot[
      f[x, y] == 1, {x, -2, 2}, {y, -2, 
        2}]
ImplicitPlot[
      Table[f[x, y] == c, {c, 0.1, 2, 0.1}], {x, -2, 
        2}, {y, -2, 2}, PlotPoints -> 100]

f[x_, y_] := x ^2  y^2/(x^2 + y^2)
Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}, PlotPoints -> 50, 
      ViewPoint -> {-1.337,  -2.473,  
          0.693}]
ImplicitPlot[
      Table[f[x, y] == c, {c, 0.1, 2, 0.1}], {x, -2, 
        2}, {y, -2, 2}]

f[x_, y_] := x ^2  y/(x^2 + y^2)
Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}, 
      PlotPoints -> 50]
ImplicitPlot[
      Table[f[x, y] == c, {c, -1, 1, 0.1}], {x, -2, 
        2}, {y, -2, 2}, PlotPoints -> 50]

Limit[f[x, y], {x -> 0, y -> 0}]

f[x_, y_] := x^2 - y^2
Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2}, PlotPoints -> 50, 
      PlotRange -> All]
ImplicitPlot[
      Table[f[x, y] == c, {c, -2, 2, 0.1}], {x, -2, 
        2}, {y, -2, 2}]

f[x_, y_, z_] := Sqrt[x^2 + y^2 + z^2]
Plot3D[
      f[x, y, 0], {x, -2, 2}, {y, -2, 2}]
Plot3D[f[x, y, 1], {x, -2, 2}, {y, -2, 2}]

Needs["Graphics`ContourPlot3D`"]

Clear[z]

f[x_, y_, z_] := Sqrt[x^2 + y^2 + z^2]
ContourPlot3D[
      f[x, y, z], {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
      Contours -> {1}]

f[x_, y_, z_] := Sqrt[x^2 + y^2 + z^2]
ContourPlot3D[
      f[x, y, z], {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
      Contours -> {2.5}, PlotPoints -> 5]

f[x_, y_, z_] := Max[Abs[x], Abs[y], Abs[z]]
ContourPlot3D[
      f[x, y, z], {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
      Contours -> {1}, PlotPoints -> 6]

f[x_, y_, z_] := x^2 + y^2 - z^2
ContourPlot3D[
      f[x, y, z], {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
      Contours -> {0}, PlotPoints -> 7]

f[x_, y_, z_] := x^2 + y^2 - z^2
ContourPlot3D[
      f[x, y, z], {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
      Contours -> {1}, PlotPoints -> 7]

ParametricPlot[{Exp[-0.1 t] Cos[t], Exp[-0.1 t] Sin[t]}, {t, 0, 
        10 Pi}, PlotRange -> All, AspectRatio -> Automatic]

ParametricPlot[{Exp[-0.1 t] Cos[t], Exp[-0.15 t] Sin[t]}, {t, 
        0, 5 Pi}, PlotRange -> All, 
      AspectRatio -> Automatic]

<< Graphics`ParametricPlot3D`

ParametricPlot3D[{Exp[-0.1 t] Cos[t], Exp[-0.02 t], 
        Exp[-0.1 t] Sin[t]}, {t, 0, 10 Pi}, PlotRange -> All, 
      PlotPoints -> 100, AspectRatio -> Automatic]

<< Graphics`PlotField`

PlotVectorField[{x, y}, {x, -2, 2}, {y, -2, 2}]

PlotVectorField[{x/Sqrt[x^2 + y^2], y/Sqrt[x^2 + y^2]}, {x, -2, 
        2}, {y, -2, 2}]

PlotVectorField[{x, -y}, {x, -2, 2}, {y, -2, 2}]

PlotVectorField[{-y, x}, {x, -2, 2}, {y, -2, 2}, 
      ColorFunction -> Hue, HeadScaling -> Relative, 
      HeadLength -> 0.4]

<< Graphics`PlotField3D`

PlotVectorField3D[{x, y, z}, {x, -2, 2}, {y, -2, 
        2}, {z, -2, 2}, VectorHeads -> True, 
      ColorFunction -> Hue, HeadScaling -> Relative, 
      HeadLength -> 0.4]

PlotVectorField3D[{y, -x, z}, {x, -2, 2}, {y, -2, 
        2}, {z, -2, 2}, VectorHeads -> True, 
      ColorFunction -> Hue, HeadScaling -> Relative, 
      HeadLength -> 0.4]