Contacts can be thought of as people your clients are associated with - wether whether they be your clients staff, consultants they have hired, or event, other project staff, or event-day staff for events your client has requested.
Multiple contacts can be associated to a client, which allows you to enter details each of the staff you may encounter at a client, as well as general contacts such as the accounting department, other managerial staff and so-on.
As a benefit to entering contacts for a client, you can then use these when entering events to specify whom the contact for an event is, as well as creating contact-log entries for later reference.
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