Although this exercise investigates the concept of time in practice you rarely deal with times on their own. They are almost always dealt with in conjunction with dates. There is no specific separate time type, only DateTime.
Time-of-day can be expressed with TimeSpan (and this is in fact the return type of DateTime.TimeOfDay). It is not purpose made so the expressiveness of code can get a bit clunky. For instance, what do you expect time-of-day to be for an instance of DateTime that is in UTC form? But, it does the job.
A discussion of time has a number of facets:
DateTime
This exercise covered local vs. UTC, date-time arithmetic, time-zones and date-time parsing.
Formatting is discussed in the string-formatting exercise.
Resolution and timers are much discussed on the web. The DateTime API has specific routines to handle file timestamps.
It's usually a good idea to store date-times long term in UTC form. This ensures consistency if more than one timezone is in play and this approach avoids potential problems with daylight saving.
The disadvantage of UTC times is that they need to be converted to local times if time-of-day is a significant factor.
For the most part DateTime.ToUniversalTime() and DateTime.ToLocalTime() work well as long as processing is based around the timezone of your computer. If multiple time zones are involved, or a different one to that of your computer then you will need the TimeZoneInfo class to handle conversions. Not the obsolete TimeZone object.
You will recall from the coding exercise that the all-important time zone identifiers differ between Windows and other platforms. This article is a good introduction to this cross-platform issue. Note that TimeZoneInfo.GetSystemTimeZones() will list your platform's time zones.
This article is a good overview of time and timezones.
For date time arithmetic, in the coding exercise, you may well have used the TimeSpan struct. When you need to do arithmetic involving whole months or years then the DateTime struct provides a number of methods such as AddHours() and AddMonths().
If dates and times are a pervasive and/or critical part of your project then you should investigate Noda Time
In case you were wondering, according to this Wikipedia article the abbreviation for universal time, UTC, arose from a compromise between English (UCT) and French (CUT) speakers such that neither language would appear to take precedence.