Abstract:
Various issues concerning the impact of inflationary models on parameter estimation from the cosmic microwave background are reviewed, with particular focus on the range of possible outcomes of inflationary models and on the amount which might be learnt about inflation from the microwave background.

Abstract:
An introductory account is given of the inflationary cosmology, which postulates a period of accelerated expansion during the Universe's earliest stages. The historical motivation is briefly outlined, and the modelling of the inflationary epoch explained. The most important aspect of inflation is that it provides a possible model for the origin of structure in the Universe, and key results are reviewed, along with a discussion of the current observational situation and outlook.

Abstract:
A brief account is given of large-scale structure modelling based on the assumption that the initial perturbations arise from inflation. A recap is made of the implications of inflation for large-scale structure; under the widely applicable slow-roll paradigm inflation adds precisely two extra parameters to the normal scenarios, which can be taken to be the tilt of the density perturbation spectrum and the amplitude of gravitational waves. Some comments are made about the {\it COBE} normalization. A short description is given of an analysis combining cosmic microwave background anisotropy data and large-scale structure data to constrain cosmological parameters, and the case of cold dark matter models with a cosmological constant is used as a specific illustration.

Abstract:
An introductory account is given of the modern understanding of the physics of the early Universe. Particular emphasis is placed on the paradigm of cosmological inflation, which postulates a period of accelerated expansion during the Universe's earliest stages. Inflation provides a possible origin for structure in the Universe, such as microwave background anisotropies, galaxies and galaxy clusters; these observed structures can therefore be used to test models of inflation. A brief account is given of other early Universe topics, namely baryogenesis, topological defects, dark matter candidates and primordial black holes.

Abstract:
The Cosmic Background Explorer (COBE) detection of microwave background anisotropies may contain a component due to gravitational waves generated by inflation. It is shown that the gravitational waves from inflation might be seen using `beam-in-space' detectors, but not the Laser Interferometer Gravity Wave Observatory (LIGO). The central conclusion, dependent only on weak assumptions regarding the physics of inflation, is a surprising one. The larger the component of the COBE signal due to gravitational waves, the {\em smaller} the expected local gravitational wave signal.

Abstract:
The energy scale of inflation is of much interest, as it suggests the scale of grand unified physics and also governs whether cosmological events such as topological defect formation can occur after inflation. The COBE results are used to limit the energy scale of inflation at around 60 $e$-foldings from the end of inflation. An exact dynamical treatment based on the Hamilton-Jacobi equations is then used to translate this into limits on the energy scale at the end of inflation. General constraints are given, and then tighter constraints based on physically motivated assumptions regarding the allowed forms of density perturbation and gravitational wave spectra. These are also compared with the values of familiar models.

Abstract:
An examination is made of the widely held belief that inflation is the only possible causal mechanism capable of generating density perturbations on scales well in excess of the Hubble radius. A simple proof is given, which relies only on the assumption that our understanding of the universe from nucleosynthesis onwards is correct. No assumption of the underlying gravitational theory is necessary beyond that it is a metric theory.

Abstract:
I explore properties of the inflationary flow equations. I show that the flow equations do not correspond directly to inflationary dynamics. Nevertheless, they can be used as a rather complicated algorithm for generating inflationary models. I demonstrate that the flow equations can be solved analytically and give a closed form solution for the potentials to which flow equation solutions correspond. I end by considering some simpler algorithms for generating stochastic sets of slow-roll inflationary models for confrontation with observational data.

Abstract:
I discuss the interplay between inflation and microwave background anisotropies, stressing in particular the accuracy with which inflation predictions need to be made, and the importance of inflation as an underlying paradigm for cosmological parameter estimation.