When Julius Caesar returned to Rome, having spent time in Egypt where he learned about the workings of their far more functional calendar from Sosigenes of Alexandria [see: Herodotus on the Egyptian Calendar], he reformed the calendar (45 B.C.). The month of Quinitilis was re-named in his honor.

In reading Roman dates, it is very useful to know a bit about the Latin grammar involved.

Here you'll find an explanation of the Latin form and the main dates of the Julian calendar.

In many cases, I leave it to you to provide the remaining, but self-explanatory (provided you know your Roman numerals and can count backwards) numerals.

Here is a self-grading quiz on the Julian Dates.

Names of the Julian Months

Each month is a mensis, so January would be mensis Januarius. The remaining month names are Februarius, Martius, Aprilis, Maius, Junius/Iunius, September, October, November, and December.

Focal Dates in the Month

The Romans didn't say it was the numbered-date {1,2,3,4,...31} of the month.

Instead, each day is expressed with respect to how long before three (must-know) lunar-based points in the month:

(1.) Kalendae (Kalends)
(2.) Nonae (Nones), and
(3.) Idus (Ides).

Agreement Between Month and Date

These three lunar-based points in the month are feminine nouns. In Latin, nouns and their adjectives have to agree in gender, number and case. So words that modify the Latin for Kalends, Nones, and Ides must be feminine and in the same number and case as the lunar words. For example, in the expression "the January Kalends" (the first day of the year), January specifies or modifies the word Kalends.

The word designating the associated month is, therefore, a feminine adjective. Dies and its related forms die and diem is the Latin for 'day'.

The Case of the Dates

The days before the three fixed points (Kalends, Nones and Ides) are, by default, expressed in the ablative case. However, certain dates -- the 4th day before the Nones of January, for example -- which could be written using the ablative case, as:

(4.) quarto die ante NonasJanuarias(5.) 4th (ablative) day (abl) before (prep.) nones (accusative) January (acc)
is more often written using the accusative case, as:

(6.) antequartum diem Nonas Januarias
Note the same preposition (ante 'before') is in #6 as in #4. In both phrases ante governs an object (diem 'day') in the Accusative Case. The difference is that it has a number attached to it in #6, but not in #4. It might help to see it divided:
(7.) ante quartum diem

Another A.D. Abbreviation
A.D. in the Modern vs. the Ancient Roman Calendar

You may be most familiar with A.D. meaning anno domini. It is used in reference to the era that follows B.C., however, in the table that follows, a.d. refers to the same die ante or ante ... [Roman numeral] ... diem shown above.
Die is in the ablative case, but diem is in the accusative case, as shown in sentences #6 and #7.
In inscriptions and other writing, you may find the date all in capital letters, so you can't count on the upper (AD) vs lower case (ad) form of a.d. to help.

Specialized Term

Pridie is a special term for a date on the Roman calendar, abbreviated Prid. It means one day before.

Source:
Augustus Samuel Wilkins' Classical Antiquities: II. Roman Antiquities.

• What Was the Format of the Roman Calendar?
• When Did We Switch Calendars?

Modern Date	Januarius/ Augustus/ December	Aprilis/ Junius/ September/ November	Martius/ Maius/ Julius/ October	Februarius
1	Kal. Jan.	Kal. Apr.	Kal. Mart.	Kal. Feb.
2	a.d. iv. Non. Jan.	a.d. iv. Non. Apr.	a.d. vi. Non. Mart.	a.d. iv. Non. Feb.
4	Prid. Non. Jan.	Prid. Non. Apr.	a.d. iv. Non. Mart.	Prid. Non. Feb.
5	Non. Jan.	Non. Apr.	a.d. iii. non. Mart.	Non. Feb.
6	a.d. viii. Id. Jan.	a.d. viii. Id. Apr.	Prid. Non. Mart.	a.d. viii. Id. Feb.
7	a.d. vii. Id. Jan.	a.d. vii. Id. Apr.	Non. Mart.	a.d. vii. Id. Feb.
8	a.d. vi. Id. Jan.	a.d. vi. Id. Apr.	a.d. viii. Id. Mart.	a.d. vi. Id. Feb.
12	Prid. Id. Jan.	Prid. Id. Apr.	a.d. iv. Id. Mart.	Prid. Id. Feb.
13	Id. Jan.	Id. Apr.	a.d. iii. Id. Mart.	Id. Feb.
14	a.d. xix. Kal. Feb.	a.d. xviii. Kal. Mai.	Prid. Id. Mart.	a.d. xvi. Kal. Mart.
15	a.d. xviii. Kal. Feb.	a.d. xvii. Kal. Mai.	Id. Mart.	a.d. xv. Kal. Mart.
16	a.d. xvii. Kal. Feb.	a.d. xvi. Kal. Mai.	a.d. xvii. Kal. Apr.	a.d. xiv. Kal. Mart.
28	a.d. v. Kal. Feb.	a.d. iv. Kal. Mai.	a.d. v. Kal. Apr.	Prid. Kal. Mart.
29	a.d. v. Kal. Feb.	a.d. iv. Kal. Mai.	a.d. v. Kal. Apr.	a.d. bis sextum Kal. Mar.
30	a.d. iii. Kal. Feb.	Prid. Kal. Mai.	a.d. iii. Kal. Apr.	--
31	Prid. Kal. Feb.	--	Prid. Kal. Apr.	--