Oracle has many built-in functions and Oracle also allows you to define your own function and make it a part of your own SQL dialect.  You can see all built-in Oracle functions with this query:

Here are my notes on common SQL built-in functions: (work in progress, more coming)

• add_months - add_months examples

• avg

• chr(n)      

• concat(s1,s2)

• convert(char_to_convert, new_char_set, old_char_set)

• count(*)     

• decode - decode examples

• floor

• greatest(expression, expression...)

• grouping

• initcap(char) string with initial capitals

• instr

• last_day(date)returns the last day of month in date

• least(expression, expression...)

• length(char)

• lower(char)   lpad(char, n[,padchar])

• ltrim(char[,set])

• max([distinct] expr)

• min([distinct] expr)

• mod(x,y)     

• months_between(end_date, start_date)

• next_day(date,day_of_week)

• nvl(expression, value_if_null)

• rank

• replace(char, search_str[, replace_str])

• round

• rowidtochar

• rpad

• rtrim

• soundex(char)

• substr

• sys_context('namespace','attribute_name')

• to_lob

• to_number

• to_date

• to_char

• translate

• trim

• trunc

• upper

• user         

• userenv

[http://www.dba-oracle.com/include_SQL_Tuning_book.htm]