This　article　presents　a　unified　description　of　numerical　methods　for　solving　electromagnetic　field　problems.　Traditionally,　these　methods　are　considered　to　be　independent　and　alternative　ways　of　solving　Maxwell＇s　equations　or　equations　derived　therefrom.　However,　they　all　are　projective　approximations　of　the　unknown　solution　by　known　expansion　or　basis　functions　with　unknown　amplitude　coefficients　that　are　determined　using　the　so-　called　method　of　weighted　residuals　(MWR).　This　common　feature　forms　the　proposed　unifying　framework　that　may　serve　both　as　a　systematic　introduction　to　computational　electromagnetics　and　as　a　way　to　provide　insight　into　the　nature,　strengths,　and　limitations　of　the　various　algorithms　used　by　present　and　future　field　solvers.　For　convenience,　the　fundamental　equations　and　concepts　of　electromagnetics　are　summarized　in　order　to　facilitate　the　demonstration　of　the　unified　approach.　Our　aim　is　to　provide　students,　designers,　and　researchers　with　a　framework　for　developing　new　numerical　algorithms,　to　guide　users　in　the　selection　and　application　of　electromagnetic　design　tools,　and　to　foster　informed　engineering　judgment.　This　article　also　serves　as　a　review　and　summary　of　earlier　theoretical　works　reported　in　different　places　and　at　different　times.　©　1963-2012　IEEE.