A nerve net is a type of nervous system that consists of many neurons but there is no brain or cephalization. Nerve nets are found in animals with radial symmetry (Cnidaria) and biradial symmetry (Ctenophora). Despite being called a net, there sometimes exist some groupings of neural cells in some Cnidaria classes, which I will write more about during the next couple of weeks.
Cnidaria are specific due to their specialized organelles, cnidocytes, which they utilize to hunt for food or use for securing itself to a surface. Some cnidocytes contain toxins that can paralyze their prey (the burning sensation you may have felt when touching a sea anemone 😉).
As a rule, Cnidaria have two diffuse nerve nets, one in the epidermal layer and a second one in the gastrodermal layer. In between these two layers is the mesoglea, a layer that functions as sort of a skeleton. The epidermal net consists of bipolar and multipolar nerve cells, while the gastrodermal net is made up of only multipolar cells.

Cnidarian nerve systems are fascinating but also quite unexplored. What is known is that nerve cells consist of two types of neurons, sensory neurons that respond to stimuli and motor neurons which ultimately trigger a response. Chemical synapses exist and provide the communication between the neurons. Hormones have also been reported in some cnidarians (steroids, neuropeptides) but it is still not known how exactly these signalling molecules work.

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In the next couple of weeks, I will write a post about every cnidarian class and also ctenophores, focusing on their nervous and sensory systems. If you have any questions or would like me to focus on something, please let me know!

Literature & more information:
^{Habdija et al: Protista-Protozoa, Metazoa-Invertebrata, Alfa, 2011, Zagreb
Endocrine-like Signaling in Cnidarians: Current Understanding and Implications for Ecophysiology
Evolution of sensory structures in basal metazoa}