The problems that were faced and solved in Athens were the sharing of political power between the established aristocracy and the emerging other classes, and the adjustment of aristocratic ways of life to the ways of life of the new polis.
词汇解释：
aristocracy: the people in the highest social class, who traditionally have a lot of land, money, and power.
emerging:in an early state of development
polis: 希腊城邦
结构分析：
复合句。主句中包含that引导的定语从句。
句子分析：
The problems(定语从句：that were faced and solved in Athens) were the sharing of political power between the established aristocracy and the emerging other classes, and the adjustment of aristocratic ways of life to the ways of life of the new polis.
主句中，the problems 是主语，。problems后接定语从句，从句中，that作主语，指的是problems，were faced and solved 是谓语， in Athens, 状语。从句后面的were the sharing…. and the adjustment…. 这些部分都是主句中的系表结构，作谓语部分。 本部分的意思是：雅典面对和解决的问题是...
表语1部分： the sharing of political power between the established aristocracy and the emerging other classes中，of political power 介词结构作定语，说明分享的是政治权利。 between the established aristocracy and the emerging other classes，依然是介词结构作定语，说明是哪两类人群在分享政治权利。本部分的意思为：现存的贵族和新兴的其他阶级之间的政治权利的分享.
表语2部分：the adjustment of aristocratic ways of life to the ways of life of the new polis. of aristocratic ways of life 定语修饰adjustment， to the ways of life of the new polis 还是定语，依然修饰adjustment，其中of the new polis 定语，修饰the ways of life. 本部分意思为：贵族们针对新城邦的生活方式对自己生活方式进行调整。
参考翻译：
雅典面对和解决的问题是：现存的贵族和新兴的其他阶级之间的政治权利的分享，以及贵族们针对新城邦的生活方式对自己的生活方式进行调整。
