Clear[f,x,y,zVal1,zVal2,zVal3];
f[x_, y_] := Cos[x^2 + y^2]
Plot3D[f[x,y], {x,-3,3},{y,-3,3}]
ContourPlot[f[x,y], {x,-3,3},{y,-3,3}]
zVal1 = -.5;zVal2 = 0; zVal3 = 0.5;

ContourPlot[f[x,y], {x,-3,3},{y,-3,3}, Contours->7,ContourShading->False ]

Show[Plot3D[f[x,y], {x,-3,3},{y,-3,3}],
Plot3D[zVal1, {x,-3,3},{y,-3,3}]]

Show[
{ContourPlot[f[x,y]==zVal1, {x,-3,3},{y,-3,3},ContourStyle->{Thick,Green,Dashing[{.03}]}, Contours->1],
ContourPlot[f[x,y], {x,-3,3},{y,-3,3}, Contours->7,ContourShading->False
  ]}]

Show[Plot3D[f[x,y], {x,-3,3},{y,-3,3}],
Plot3D[zVal2, {x,-3,3},{y,-3,3}]]

Show[
{ContourPlot[f[x,y]==zVal2, {x,-3,3},{y,-3,3},ContourStyle->{Thick,Green,Dashing[{.03}]}, Contours->1],
ContourPlot[f[x,y], {x,-3,3},{y,-3,3}, Contours->7,ContourShading->False
  ]}]

Show[Plot3D[f[x,y], {x,-3,3},{y,-3,3}],
Plot3D[zVal3, {x,-3,3},{y,-3,3}]]

Show[
{ContourPlot[f[x,y]==zVal3, {x,-3,3},{y,-3,3},ContourStyle->{Thick,Green,Dashing[{.03}]}, Contours->1],
ContourPlot[f[x,y], {x,-3,3},{y,-3,3}, Contours->7,ContourShading->False
  ]}]