Discourse analysis

Man and mankind have traditionally been used for the human race.
Why does man have more diseases than animals?
That's one small step for a man, one giant leap for mankind.
(Neil Armstrong, on stepping onto the moon)
Some people find this usage sexist, and prefer terms such as people, humanity or the human race. Note also the common use of synthetic instead of man-made.
Titles
Ms (pronounced /mlz/ or /maz/) is often used instead of Mrs or Miss. Like Mr, it does not show whether the person referred to is married or not

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  Developing 'Gender-Neutral' vocabulary. We can see this as one attempt to rid the language of gender bias in the sense that such words either replace a male-specific item (e.g. fire fighter for fireman) or deny the necessity to mark the gender of the occupant of a particular post (e.g. headteacher for headmaster or headmistress).
  

NOTE: A mayor can be a man or a woman; in Britain a mayoress is the wife of a male
Mayor. One example related to the power of social pressure to bring about language change is the increasingly frequent use of the word partner to refer to the person with whom one has a close personal relationship (a kind of life partner, perhaps, rather than a business partner¹). It implies an equality of status between married and unmarried relationships and, because it is not gender-specific, it bestows similar equality on same-sex and mixed-sex relationships. The use of this word with this meaning certainly reflects attitude changes in some societies towards gender relations.

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  (unisex- they). In an informal style, we often use they to mean 'he or she', especially after
  

indefinite words like somebody, anybody, nobody, person. This usage is
sometimes considered 'incorrect', but it has been common in educated speech for centuries.
If anybody wants my ticket, they can have it.
There's somebody at the door. ~ Tell them I'm out.
When a person gets married, they have to start thinking about their responsibilities.