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Back in year 3…In the Roman world, which consisted of most of Europe and its colonies, from 45 BC to to the introduction of the modern Gregorian calendar in 1582 (although it took several centuries to fully implement it), the primary calendar was the Julian calendar. It is almost exactly the same as the Gregorian calendar, with one exception.The exception is that in the new Gregorian calendar, every century that was not a multiple of 400 would not be a leap year. Thus, 1700, 1800, and 1900 were all “regular” years, but 2000 was a leap year. Using the Julian calendar, which adds a leap year every 4 years with no exceptions, 1700, 1800, and 1900 would all be leap years. This small difference made the Julian calendar less accurate than the Gregorian one.The year in Julian calendars is pretty much exactly the same as in Gregorian calendars, except that the Julian calendar is a few weeks slower than the Gregorian. So 2017 would be something more akin to late December 2016 - early December 2017. Not perfectly aligned, but close enough.In Han China at this time, from sometime within Emperor Wu’s reign (141 BC - 87 BC) all the way to the use of the Chongzhen/Shixian calendar developed in the 17th century, the Taichu or Grand Inception Calendar (太初曆) was used. Wikipedia defines it thus:[Wu’s] Taichu or Grand Inception Calendar (traditional Chinese: 太初曆; simplified Chinese: 太初历) introduced 24 solar terms which determined the month names. The solar year was defined as 365 [math]\frac{385}{1539}[/math] days, and divided into 24 solar terms. Each couples of solar terms are associated into 12 climate terms. The lunar month was defined as 29 [math]\frac{43}{81}[/math] days and named according to the closest climate term. The mid-climate in the month decides the month name, and a month without mid-climate is an intercalary month.Source: Chinese calendar - WikipediaIn Egypt at the time, the Coptic calendar was used. Formally adopted by Emperor Augustus in 25 BC, it is still used today. The year starts on 11 (or 12) September, the 365 (or 366) days spread out over 12 normal months of 30 days each and an intercalary (catch-up) month of 5 to 6 days depending on the (leap) year. See Intercalary month (Egypt) - Wikipedia for more details on this month. The months are further divided into 3 seasons of 4 months each. The intercalary month is at the very end of the 5-month Season of the Harvest. Leap years are every 4 years without exception, just like the Julian calendar.Since the Coptic calendar starts at the year 284, it is unclear what year 3 would be called, but year 2017 would start in year 1733 AM (Anno Martyrum, named for Diocletian’s (reign started AD 284) bloody persecution of Christians) and end in early 1734.In India, several Hindu calendars, or Panchanga (पञ्चाङ्ग) were used, among these the Bikrami calendar, Tamil calendar, and Bengali calendar. They focused on the lunar cycles, and their new year started in spring (April). Each month started and ended during either a new or full moon, each month being subdivided into two paks(h)a (पक्ष).Different Hindu calendars place the starting year at different dates; a common base year is AD 78, the start of the Saka era. Another base year is Vikram Samvat, around 57 BC. As a result, 2017 is 1939 by the Saka calendar and 2073-2074 in the Vikram Samvat calendar.Many other calendars were used in many other places, but their details are either so unclear, or too complicated. Therefore I will not include them in this answer. Almost all my information was gathered on various pages from Template:Calendars - Wikipedia, so feel free to check them out.