What is a Battery?

A battery is an electrochemical device that converts chemical energy into electricity, by use of a galvanic cell.

What is a Fuel Cell? 

A fuel cell converts the chemical energy of hydrogen and oxygen directly to produce electricity and its byproducts water and heat.   
    
Electrochemistry Courses @ MIT
   
    2.625/10.625
     Electrochemical Energy Conversion and Storage: Fundamentals, Materials and Applications
     Instructor : Yang Shao-Horn
   
     3.53
      Electrochemical Processing of Materials
     Instructor : Donald R. Sadoway  
       
Links
 
             
          Advanced Materials

           
                   Nature 

             
                  Science
           
           Nature Materials
     
                Journal of
        Electrochemical Society		               
    Journal of the American 
          Chemical Society 		             
   Angewandte Chemie
       International Edition		              
      Chemistry of Materials