Marriage
It could be argued that the rejection of marriage is the central didactic point of this novel. Hardy repeatedly emphasizes that marriage involves making a commitment that many people are emotionally unequipped to fulfill - this sentiment comes from the narrator, but it is also expressed by Sue, Jude, Phillotson, and Widow Edlin at various points in the novel. Whether the institution of marriage can be saved is open to interpretation. Jude and Sue are clearly a good match for each other, so Jude wants to get married. Sue, however, feels that marriage will poison the relationship. The narrator does not seem to favor either side; it is left up to readers to decide how the problems with marriage might be solved.
Education
Hardy highlights many kinds of education in Jude the Obscure. Most obviously, we have Jude's desire to get a university degree and become an academic. However, Hardy also emphasizes the importance of experiential education. Because Jude is inexperienced with women and with social situations more generally, he is especially susceptible to Arabella's seduction. In the novel, the level of traditional education one reaches is closely tied to the class system, and if someone from Jude's class wants to learn, they must teach themselves. Although the narrator seems to admire Jude's willingness to teach himself, he also points out the limits of autodidacticism, noting that despite Jude's near-constant studies, he cannot hope to compete on the university entrance exam against richer men who have hired tutors.
Religion
As Jude the Obscure can be interpreted as critical of the institution of marriage, Hardy is equally as possessed with the church. Throughout their relationship, Jude and Sue have many conversations concerning religion, the former being initially more devout than his intellectually curious cousin. At a diorama depicting Jerusalem, the major characters' feelings on religion crystalize. Sue wonders why Jerusalem rather than Rome or Athens is deemed important, Phillotson counters that the city is important to the English as a Christian people, and Jude is utterly absorbed by the work - though he also strains to agree with Sue. Later, Sue mentions a friend who was the most irreligious but also the most moral. Hardy points out that these concepts are not mutually exclusive.
Jude's faith is tested by Sue. He realizes his sexual attraction to her makes him a hypocrite. Rather than suppress his natural physical desire, he burns his books, marking his break with Christianity. This makes Sue's reversal later in the novel all the more shocking. Jude likens her conversion in the wake of her children's death to his partaking in alcohol during difficult times. Here Hardy calls into question the motivations behind faith. Through Sue's self-punishing adherence to her Christian duties despite her true nature, Hardy suggests those motivations are not always pure.
Women's rights
Sue Bridehead is a strikingly modern heroine in many ways - she lives with men without marrying them; she has a rich intellectual life; she works alongside Jude. Hardy criticizes the social conventions that prevent her from fulfilling her potential as an intellectual and as a worker. However, he also reinforces some of those social conventions unintentionally; by portraying Sue as anxious and hysterical, Hardy perpetuates a common Victorian stereotype about women being especially emotional. Also, we are expected to accept Sue having lived with the Christminster undergraduate because they were not having sex; despite his professed liberalism, Hardy upholds traditional values by offering this piece of information and (apparently) expecting it to color our judgment of the character.
Old versus new
The narrator of Jude the Obscure often laments the ways that old things are replaced by the new, especially when it comes to urban architecture. Likewise, the Widow Edlin suggests that older, more laid-back attitudes toward marriage are better than prudish Victorian norms. Nineteenth-century British society was, in many ways, more conservative than the historical periods that preceded it, so Hardy's admiration for the older aspects of English culture ties in to his social liberalism and his reverence for intellectual inquiry.
Disappointment
Disappointment crops up over and over again in this novel: Jude is disappointed by his career; he is disappointed in his marriage to Arabella and then his cohabitation with Sue; he is disappointed by Mr. Phillotson, who never achieved his dream of getting a university degree. Even Time's assertions that he never asked to be born suggest a certain disappointment with life. Since most of the novel's tragedies come as lost opportunities, the ways that the characters deal with disappointment contribute to their characterization. For example, Phillotson takes a relatively mature perspective when he is disappointed in his marriage to Sue, and allows her to be with Jude. Arabella, in contrast, deals with her disappointment in Cartlett by spying on Jude and scheming to get back together with him.
Itinerancy
Jude the Obscure features many kinds of nomads. Some of these are minor characters, like the traveling laborers in Shaston. However, Jude himself is a kind of nomad, and the novel's structure reflects this. It is not divided into arbitrary chapters or thematic groupings, but rather is divided into sections based on the characters' location. This geographical mobility speaks to the new freedom - but also rootlessness - that came with the advent of rail travel, which revolutionized the lives of working people like Jude, who could now travel long distances affordably.
Social class
In addition to his points about education, Hardy also criticizes the rigidity of social class more generally. Jude is limited in his career options because as a working-class man, he cannot hope to be promoted beyond a certain level, even in fields like the clergy that are supposed to be open to all. However, Jude and Sue also benefit from their low social class in that their respective divorces are processed quickly and without inquiry and they can get away with living together unmarried for quite some time. Even this is a mixed blessing - they are caught eventually, and the reason they weren't caught sooner is that they are unimportant to the people around them.