Have a look at perlfunc (you can type man perlfunc or perldoc perlfunc as well). A portion from the top:

       Perl Functions by Category

       Here are Perl's functions (including things that look like func
+tions, like some keywords and
       named operators) arranged by category.  Some functions appear i
+n more than one place.

       Functions for SCALARs or strings
           "chomp", "chop", "chr", "crypt", "hex", "index", "lc", "lcf
+irst", "length", "oct", "ord",
           "pack", "q/STRING/", "qq/STRING/", "reverse", "rindex", "sp
+rintf", "substr", "tr///",
           "uc", "ucfirst", "y///"

      <snip>
 
       Functions for real @ARRAYs
           "pop", "push", "shift", "splice", "unshift"

       Functions for list data
           "grep", "join", "map", "qw/STRING/", "reverse", "sort", "un
+pack"
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Also note that for specific funcitons (e.g. grep), you can do perldoc -f grep to see just that section of perlfunc.