eightsurface[u_, v_] := {Cos[u] Cos[v] Sin[v], Sin[u] Cos[v] Sin[v], 
        Sin[v]}

ParametricPlot3D[
      eightsurface[u, v], {u, 0, 2  Pi}, {v, 0, 2  Pi}]

ParametricPlot3D[eightsurface[u, v], {u, 0, 2  Pi}, {v, 0, 2  Pi}, 
      ViewPoint -> {0, 0, 2}]

ParametricPlot3D[eightsurface[u, v], {u, 0, 2  Pi}, {v, 0, 2  Pi}, 
      ViewPoint -> {0, 2, 0}, PlotPoints -> 20]

ParametricPlot3D[eightsurface[u, v], {u, 0, 2  Pi}, {v, 0, 2  Pi}, 
      PlotPoints -> 20, Boxed -> False,  
      Axes -> None]

Plot3D[x^2 + y^2, {x, -10, 10}, {y, -10, 10}, 
      Axes -> None]

Iperboloide[u_, v_] := {u, v, u v}

ParametricPlot3D[Iperboloide[u, v], {u, -10, 10}, {v, -10, 10}, 
      PlotPoints -> 20, Boxed -> False,  Axes -> None, 
      AspectRatio -> 1.2]

Plot3D[x y, {x, -10, 10}, {y, -10, 10}, 
      ViewPoint -> {2, -4, 0}, AspectRatio  -> 1.2]

monkeysaddle[u_, v_] := {u, v, u^3 - 3  u v^2}

ParametricPlot3D[
      monkeysaddle[u, v], {u, -10, 10}, {v, -10, 10}, 
      PlotPoints -> 40, Boxed -> False,  Axes -> None, 
      AspectRatio -> 1.2]

Ellissoidi

Plot3D[{Sqrt[
          1 - 2  x^2 - 3  y^2], -Sqrt[1 - 2  x^2 - 3  y^2]}, {x, -1, 
        1}, {y, -1, 1}, PlotPoints -> 40]

ellipsoid[u_, v_] := {2  Cos[u] Cos[v], 3  Cos[v] Sin[u], 
        4  Sin[v]}

ParametricPlot3D[
      ellipsoid[u, v], {u, 0, 2  Pi}, {v, 0, 2  Pi}]

stereoellis[u_, v_] := {2  u/(1 + u^2 + v^2), 
        6  v/(1 + u^2 + v^2), 
        4 (v^2 + u^2 - 1)/(1 + u^2 + v^2)}

ParametricPlot3D[
      stereoellis[u, v], {u, -5.5, 5.5}, {v, -5.5, 5.5}, 
      PlotRange -> {{-3, 3}, {-3, 3}, {-6, 6}}, 
      AspectRatio -> Automatic, PlotPoints -> 30]

?PlotRange

TORI

toro[u_, 
        v_] := {(8 + 3  Cos[v]) Cos[u], (8 + 3  Cos[v]) Sin[u], 
        7  Sin[v]}

ParametricPlot3D[toro[u, v], {u, 0, 2  Pi}, {v, 0, 2  Pi}, 
      AspectRatio -> Automatic, PlotPoints -> 30, 
      ViewPoint -> {2, 2, 2}]

SUPERFICI DI ROTAZIONE

x[{p1_, p2_}] := p1

    y[{p1_, p2_}] := p2

    rotaz[alpha_][u_, v_] := {x[alpha[u]] Cos[v], x[alpha[u]] Sin[v], 
        y[alpha[u]]}

eight[t_] := {Sin[t] Cos[t], Sin[t]}
eight1[t_] := {Sin[t], Cos[t] Sin[t]}

ParametricPlot[
      eight1[t], {t, 0, 2  Pi}]

ParametricPlot3D[rotaz[eight1][u, v], {u, 0, 2  Pi}, {v, 0, 2  Pi}, 
      ViewPoint -> {0, 0, 3}]

ParametricPlot3D[rotaz[eight][u, v], {u, 0, 2  Pi}, {v, 0, 2  Pi}, 
      ViewPoint -> {1, 2, 3}]

Caten[t_] := {Cosh[t], t}

ParametricPlot[Caten[t], {t, -3, 3}, 
      PlotRange -> {{-3, 3}, {-3, 3}}]

ParametricPlot3D[rotaz[Caten][u, v], {u, -1, 1}, {v, 0, 
        2  Pi}]

sufsin[u_, v_] := {Sin[u], Sin[v], Sin[u + v]}

ParametricPlot3D[sufsin[u, v], {u, 0, 2  Pi}, {v, 0, 2  Pi}]