We have intelligence from Mexico to the 25th of January. Congress assembled on the 1st. The President opened the session by a speech about an hour in length. He says that the stipulations of the treaty of peace with the United States have been faithfully observed, and have proved highly advantageous for Mexico. Three treaties have been concluded during his administration--one with the United States in regard to the Isthmus of Tehuantepec, another with the same power concerning the extradition of criminals, and another with Guatemala on the same subject. Domestic tranquillity has been preserved throughout the country; complaint, however, is made that the States transcend their rightful authority, and thus weaken the General Government; and the necessity of providing a remedy for this abuse, in order to maintain the integrity of the Federal Constitution, is strongly urged. Commerce and manufactures are said to have flourished, and the mining business, which is the chief resource of Mexico, has been peculiarly good. Their entire returns during the last year are estimated at thirty millions. The President urges the propriety of making laws to restrain the licentiousness of the press. The army has been thoroughly reformed, consisting now of only 6246 men, all of whom are characterized as "true soldiers," stationed in places where their services will be most useful to the Republic. On the 15th, Gen. Arista was inaugurated President of Mexico. His opening address was brief, pertinent, and patriotic. He spoke of peace as the first necessity of the Republic, and promised that it should be "maintained at any cost, as the only manner in which the happiness and prosperity of the people can be secured." He says that "every thing will be done by the central authorities to enable the States to equalize the expenses and their revenues; to multiply their ways of communication; to augment their agricultural and commercial industry; in short, to make them great and powerful, attracting to their bosoms the intelligent, industrious and enlightened population which they so much need." The address was received with great satisfaction. The ceremony of the inauguration was extremely brilliant, and was witnessed by an immense concourse of people. After it was over, the President and his ministers repaired to the cathedral, where a _Te Deum_ was sung, and prayers offered up for the happiness of the nation. The personal popularity of Gen. Arista is very great, and the best hopes are indulged of his administration.