Some frequently used commands:
( See more what you can do with
Mathematica) 
Plot[ x Sin[x],{x,10,10}]  Graph function of one variable 
Plot3D[ Sin[x y],{x,2,2},{y,2,2}]  Graph function of two variables 
ParametricPlot[ {Cos[3 t],Sin[5 t]} ,{t,0,2Pi}]  Plot planar curve 
ParametricPlot3D[ {Cos[t],Sin[t],t} ,{t,0,4Pi},AspectRatio>1]  Plot space curve 
ParametricPlot3D[ {Cos[t] Sin[s],Sin[t] Sin[s],Cos[s]},{t,0,2Pi},{s,0,Pi}]  Parametric Surface 
ContourPlot[ Sin[x y],{x,2,2},{y,2,2} ]  Contour lines (traces) 
Integrate[ x Sin[x], x]  Integrate symbolically 
NIntegrate[ Exp[x^2],{x,0,10}]  Integrate numerically 
D[ Cos^5[x],x ]  Differentiate symbolically 
Series[Exp[x],{x,0,3} ]  Taylor series 
DSolve[ x''[t]==x[t],x,t ]  Solution to ODE 
Get["Graphics`ContourPlot3D`"];
ContourPlot3D[x^2+2y^2z^21,{x,2,2},{y,2,2},{z,2,2}]  Implicit surface 
ClassifyCriticalPoints[f_,{x_,y_}] := Module[{X,P,H,g,d,S},
X={x,y}; P=Solve[Thread[D[f,#] & /@ X==0],X];H=Outer[D[f,#1,#2]&,X,X];g=H[[1,1]];d=Det[H];
S[d_,g_]:=If[d<0,"saddle",If[g>0,"minimum","maximum"]];
TableForm[{x,y,d,g,S[d,g],f} /. Sort[P],TableHeadings>{None,{x,y,"D","f_xx","Type","f"}}]]
ClassifyCriticalPoints[4 x y  x^3 y  x y^3,{x,y}]
