The Rama concludes Shulchan Aruch Orach Chaim (697:1) with a discussion of our obligation to increase drinking and joy on Purim Katan, the 14th day of Adar Rishon. He rules that there is no obligation to do so, but one should add a bit to his meal. The Rama's final words are: "A good-hearted person feasts perpetually" (Mishlei 15:15). This implies that the requirement to increase joy "from when Adar enters" (Ta'anis 29a) applies to Adar Rishon as well, and the Gemara (29b) further states that one enjoys good luck and should adjudicate any outstanding cases with non-Jews in their courts at that time (Mishna Berurah 686:8). The increase in joy is left undefined, however, and requires explanation.
The Vilna Gaon contrasts the above phrase in Mishlei with the first half of the pasuk: "All the days of a poor man are bad." Chazal teach us that, "Who is wealthy? One who is happy with his portion" (Avos 4:1). The poor man referred to is one who is never happy because he has a greedy soul and always covets more (see Avos 5:23, 4:28), and therefore all his days are bad; even when successful, he desires more and is therefore unhappy. By contrast, one who is satisfied with what he has is always happy. One who drinks is happy only while he is intoxicated, but not after the effects of alcohol wear off. One who is good-hearted is always as happy as the one who drinks is at the time of drinking. A good heart is the most important attribute (Avos 2:13, Vilan Gaon), and enables a person to always be happy.
Why is Adar a time to increase joy? Rashi (29a) explains "From when Adar enters" as follows: "Purim and Pesach were days of miracles for Yisroel". On a simple level, Rashi is saying that one's joy increases upon remembering that Am Yisroel experienced miracles in Adar and Nissan many years ago. However, the cause of the joy goes beyond merely remembering the past. True joy occurs when one is happy with his portion. Remembering the miracles Hashem performed for Am Yisroel during these months reminds us that Am Yisroel is Hashem's portion (Devarim 32:9). This enables us to be happy despite whatever problems we face. Moreover, the juxtaposition of Purim and Pesach, which is the reason we celebrate Purim in Adar Sheni (Megilla 6b), represents a critical lesson. Just as the open miracles of Pesach are clearly divinely ordained, so too is the hidden miracle of Purim.
"From the great and open miracles one acknowledges the hidden miracles which are fundamentals of the entire Torah. We have no portion (chelek) in the Torah of Moshe Rabeinu until we believe that all our matters and occurrences are all miracles. None are nature and the way of the world, neither those of the community nor those of the individual" (Ramban Shemos 13:16).
Joy increases in Adar when we internalize this crucial lesson. We exalt in our being Hashem's portion, which began, as a nation, with the events recalled on Pesach. We begin our joy in Adar, when we celebrate the hidden miracle of Purim and focus on the Ramban's idea that all of our personal matters are ordained by Hashem.
We can be happy with our lot if we recognize that it is controlled from Above. On Purim, the festival of lots, this recognition reaches its peak, and the month of Adar leads up to the peak with increasing joy.
The absence of Purim in Adar Rishon is due to the need to have Purim and Pesach in adjacent months. This reminds us that hidden miracles, and all of our matters, are the result of Divine Providence. We thereby increase joy from the beginning of Adar Rishon, and on Purim Katan we reach the level of "A good-hearted person feasts perpetually." By contrast, we reduce joy from when Av enters (Ta'anis 29a).
On a simple level the sadness of Tisha B'Av comes from our recalling the destruction of the Temples and other tragedies. However, the original sin of Tisha B'Av was caused by a failure to recognize the universal nature of Divine Providence. "The people wept on that night" (Bamidbar 14:1), they cried on Tisha B'Av after hearing the report of the spies detailing the power of the enemy forces in Eretz Yisroel. "They are too strong for us" (13:31), and even, as it were, for Him (Rashi). Hashem responded: "How long will they not have faith in Me, despite all the miracles I have performed in their midst?" (14:11). Am Yisroel indeed saw the open miracles in Egypt and beyond, but they knew that in Eretz Yisroel they would lead a natural life and they did not realize that Divine Providence extends beyond supernatural events into the hidden miracles of every day. This failure caused them to cry notwithstanding the great miracles of the Exodus and the ongoing blessings they experienced in the desert. All the days of the poor are bad, even successful ones, if he does not recognize that the blessings are from Hashem. We reduce joy from the beginning of Av because in that month the secret of joy, the belief that our portion and our fate is always in Hashem's hands, was forgotten.
Rejoicing in our portion results from our having a portion in the Torah of Moshe Rabeinu and realizing that our portion is determined by Hashem. Every Shabbos we pray for our unique portion in Hashem's Torah. On this Shabbos, Rosh Chodesh Adar Rishon, we begin to increase joy by reinforcing our faith in hashgacha pratis upon Am Yisroel and each individual, from the events of Purim and Pesach until this very day.